4565:
4573:
4557:
4549:
1977:
11449:
8263:
2159:
1079:
1479:
4458:
produce the harmonic mean of the other ā i.e., converting the mean value of fuel economy expressed in litres per 100 km to miles per gallon will produce the harmonic mean of the fuel economy expressed in miles per gallon. For calculating the average fuel consumption of a fleet of vehicles from the individual fuel consumptions, the harmonic mean should be used if the fleet uses miles per gallon, whereas the arithmetic mean should be used if the fleet uses litres per 100 km. In the USA the
4095:(P/E). If these ratios are averaged using a weighted arithmetic mean, high data points are given greater weights than low data points. The weighted harmonic mean, on the other hand, correctly weights each data point. The simple weighted arithmetic mean when applied to non-price normalized ratios such as the P/E is biased upwards and cannot be numerically justified, since it is based on equalized earnings; just as vehicles speeds cannot be averaged for a roundtrip journey (see above).
809:
11435:
3791:'s weighted by their respective distances (optionally with the weights normalized so they sum to 1 by dividing them by trip length). This gives the true average slowness (in time per kilometre). It turns out that this procedure, which can be done with no knowledge of the harmonic mean, amounts to the same mathematical operations as one would use in solving this problem by using the harmonic mean. Thus it illustrates why the harmonic mean works in this case.
2065:
6036:
4488:
3805:
3075:
1999:
1972:{\displaystyle H\left(x_{1},\ldots ,x_{n}\right)={\frac {\left(G\left(x_{1},\ldots ,x_{n}\right)\right)^{n}}{A\left(x_{2}x_{3}\cdots x_{n},x_{1}x_{3}\cdots x_{n},\ldots ,x_{1}x_{2}\cdots x_{n-1}\right)}}={\frac {\left(G\left(x_{1},\ldots ,x_{n}\right)\right)^{n}}{A\left({\frac {1}{x_{1}}}{\prod \limits _{i=1}^{n}x_{i}},{\frac {1}{x_{2}}}{\prod \limits _{i=1}^{n}x_{i}},\ldots ,{\frac {1}{x_{n}}}{\prod \limits _{i=1}^{n}x_{i}}\right)}}.}
4258:
11473:
11461:
499:
5413:
7621:
4363:, while number of negatives, in general, is large and unknown. It is thus a trade-off as to whether the correct positive predictions should be measured in relation to the number of predicted positives or the number of real positives, so it is measured versus a putative number of positives that is an arithmetic mean of the two possible denominators.
4949:
3470:
484:
804:{\displaystyle {\begin{aligned}H(x_{1},x_{2},\ldots ,x_{n})&={\frac {1}{\displaystyle A\left({\frac {1}{x_{1}}},{\frac {1}{x_{2}}},\ldots {\frac {1}{x_{n}}}\right)}},\\A(x_{1},x_{2},\ldots ,x_{n})&={\frac {1}{\displaystyle H\left({\frac {1}{x_{1}}},{\frac {1}{x_{2}}},\ldots {\frac {1}{x_{n}}}\right)}},\end{aligned}}}
5187:
3869:
given the densities of its constituent elements and their mass fractions (or, equivalently, percentages by mass), then the predicted density of the alloy (exclusive of typically minor volume changes due to atom packing effects) is the weighted harmonic mean of the individual densities, weighted by
3774:
However, one may avoid the use of the harmonic mean for the case of "weighting by distance". Pose the problem as finding "slowness" of the trip where "slowness" (in hours per kilometre) is the inverse of speed. When trip slowness is found, invert it so as to find the "true" average trip speed. For
7374:
1429:
7948:
4457:
two measures are commonly used ā miles per gallon (mpg), and litres per 100 km. As the dimensions of these quantities are the inverse of each other (one is distance per volume, the other volume per distance) when taking the mean value of the fuel economy of a range of cars one measure will
211:
8199:
7255:
3770:
is needed. For the arithmetic mean, the speed of each portion of the trip is weighted by the duration of that portion, while for the harmonic mean, the corresponding weight is the distance. In both cases, the resulting formula reduces to dividing the total distance by the total time.)
4788:
3256:
293:
5063:
4415:
values for a flow that is perpendicular to layers (e.g., geologic or soil) - flow parallel to layers uses the arithmetic mean. This apparent difference in averaging is explained by the fact that hydrology uses conductivity, which is the inverse of resistivity.
2178:
to calculate it. The blue line shows that the harmonic mean of 6 and 2 is 3. The magenta line shows that the harmonic mean of 6 and ā2 is ā6. The red line shows that the harmonic mean of a number and its negative is undefined as the line does not intersect the
4678:
3059:
4404:. That is, the appropriate average for the two types of pump is the harmonic mean, and with one pair of pumps (two pumps), it takes half this harmonic mean time, while with two pairs of pumps (four pumps) it would take a quarter of this harmonic mean time.
4366:
A consequence arises from basic algebra in problems where people or systems work together. As an example, if a gas-powered pump can drain a pool in 4 hours and a battery-powered pump can drain the same pool in 6 hours, then it will take both pumps
7039:
1216:
5408:{\displaystyle {\begin{aligned}\lim _{\beta \to 0}H_{1-X}&={\text{ undefined }}\\\lim _{\beta \to 1}H_{1-X}&=\lim _{\alpha \to \infty }H_{1-X}=0\\\lim _{\alpha \to 0}H_{1-X}&=\lim _{\beta \to \infty }H_{1-X}=1\end{aligned}}}
1057:
7347:
6001:
7616:{\displaystyle {\begin{aligned}H_{1}&={\frac {n}{\sum \left({\frac {1}{x}}\right)}}\\H_{2}&={\frac {\left(\exp \left\right)^{2}}{{\frac {1}{n}}\sum (x)}}\\H_{3}&=\exp \left(m-{\frac {1}{2}}s^{2}\right)\end{aligned}}}
7811:
1433:
Since the harmonic mean of a list of numbers tends strongly toward the least elements of the list, it tends (compared to the arithmetic mean) to mitigate the impact of large outliers and aggravate the impact of small ones.
2914:
7126:
929:
6174:
56:
7976:
7774:
7148:
4442:, the harmonic mean is used when calculating the effects of fluctuations in the census population size on the effective population size. The harmonic mean takes into account the fact that events such as population
2414:
4473:
the average mass per particle of a mixture consisting of different species (e.g., molecules or isotopes) is given by the harmonic mean of the individual species' masses weighted by their respective mass fraction.
6300:
1198:
is always in between. (If all values in a nonempty data set are equal, the three means are always equal to one another; e.g., the harmonic, geometric, and arithmetic means of {2, 2, 2} are all 2.)
6470:
5515:
2598:
4944:{\displaystyle {\begin{aligned}\lim _{\alpha \to 0}H&={\text{ undefined }}\\\lim _{\alpha \to 1}H&=\lim _{\beta \to \infty }H=0\\\lim _{\beta \to 0}H&=\lim _{\alpha \to \infty }H=1\end{aligned}}}
2320:
3465:{\displaystyle H={\frac {\sum \limits _{i=1}^{n}w_{i}}{\sum \limits _{i=1}^{n}{\frac {w_{i}}{x_{i}}}}}=\left({\frac {\sum \limits _{i=1}^{n}w_{i}x_{i}^{-1}}{\sum \limits _{i=1}^{n}w_{i}}}\right)^{-1}.}
479:{\displaystyle H(x_{1},x_{2},\ldots ,x_{n})={\frac {n}{\displaystyle {\frac {1}{x_{1}}}+{\frac {1}{x_{2}}}+\cdots +{\frac {1}{x_{n}}}}}={\frac {n}{\displaystyle \sum _{i=1}^{n}{\frac {1}{x_{i}}}}}.}
5739:
6613:
5149:
6237:
5598:
7981:
7816:
7379:
6819:
5192:
4793:
504:
6374:
1444:
The harmonic mean is related to the other
Pythagorean means, as seen in the equation below. This can be seen by interpreting the denominator to be the arithmetic mean of the product of numbers
7685:
4970:
4750:
4446:
increase the rate genetic drift and reduce the amount of genetic variation in the population. This is a result of the fact that following a bottleneck very few individuals contribute to the
6724:
5885:
6535:
4598:
2941:
2475:
285:
6907:
3950:
As with the previous example, the same principle applies when more than two resistors, capacitors or inductors are connected, provided that all are in parallel or all are in series.
2528:
1070:, which is an even stronger property than Schur-concavity. One has to take care to only use positive numbers though, since the mean fails to be concave if negative values are used.
2636:
8876:
2152:
5672:
3525:(30 km/h), not the arithmetic mean (40 km/h). The total travel time is the same as if it had traveled the whole distance at that average speed. This can be proven as follows:
3870:
mass, rather than the weighted arithmetic mean as one might at first expect. To use the weighted arithmetic mean, the densities would have to be weighted by volume. Applying
4254:, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD. Then FG is the harmonic mean of AB and DC. (This is provable using similar triangles.)
2689:
4327:(the distance from a focus to the ellipse along a line parallel to the minor axis) is the harmonic mean of the maximum and minimum distances of the ellipse from a focus.
8509:
Da-Feng Xia, Sen-Lin Xu, and Feng Qi, "A proof of the arithmetic mean-geometric mean-harmonic mean inequalities", RGMIA Research Report
Collection, vol. 2, no. 1, 1999,
4564:
4572:
6945:
4316:
are measured as distances from the floor along lines parallel to the walls. This can be proved easily using the area formula of a trapezoid and area addition formula.
1985:ā that is, two or more elements of the set are "spread apart" from each other while leaving the arithmetic mean unchanged ā then the harmonic mean always decreases.
3244:
3217:
3190:
3163:
2778:
2751:
2724:
2239:
2212:
940:
9069:
3953:
The "conductivity effective mass" of a semiconductor is also defined as the harmonic mean of the effective masses along the three crystallographic directions.
7266:
5896:
8741:
Agrrawal, Pankaj; Borgman, Richard; Clark, John M.; Strong, Robert (2010). "Using the Price-to-Earnings
Harmonic Mean to Improve Firm Valuation Estimates".
1424:{\displaystyle H\left(x_{1},x_{2},\ldots ,x_{n}\right)=M_{-1}\left(x_{1},x_{2},\ldots ,x_{n}\right)={\frac {n}{x_{1}^{-1}+x_{2}^{-1}+\cdots +x_{n}^{-1}}}}
7943:{\displaystyle {\begin{aligned}\operatorname {bias} \left&={\frac {HC_{v}}{n}}\\\operatorname {Var} \left&={\frac {H^{2}C_{v}}{n}}\end{aligned}}}
8635:
2786:
8973:
Cox DR (1969) Some sampling problems in technology. In: New developments in survey sampling. U.L. Johnson, H Smith eds. New York: Wiley
Interscience
7063:
9007:
Akman O, Gamage J, Jannot J, Juliano S, Thurman A, Whitman D (2007) A simple test for detection of length-biased sampling. J Biostats 1 (2) 189-195
817:
206:{\displaystyle \left({\frac {1^{-1}+4^{-1}+4^{-1}}{3}}\right)^{-1}={\frac {3}{{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{4}}}}={\frac {3}{1.5}}=2\,.}
6642:). Assume also that the likelihood of a variate being chosen is proportional to its value. This is known as length based or size biased sampling.
6110:
8194:{\displaystyle {\begin{aligned}{\frac {H\log _{e}\left(1+C_{v}\right)}{2n}}\left\\{\frac {H\log _{e}\left(1+C_{v}\right)}{n}}\left\end{aligned}}}
7250:{\displaystyle \operatorname {E} \left(X^{-1}\right)\geq {\frac {\operatorname {E} \left(X^{n-1}\right)}{\operatorname {E} \left(X^{n}\right)}}.}
10570:
8925:
Aitchison J, Brown JAC (1969). The lognormal distribution with special reference to its uses in economics. Cambridge
University Press, New York
7691:
11075:
3904:(e.g., 40 Ī©), then the effect is the same as if one had used two resistors with the same resistance, both equal to the harmonic mean of
2325:
6321:
method of estimating the variance is possible if the mean is known. This method is the usual 'delete 1' rather than the 'delete m' version.
6251:
4556:
2639:
4280:, where two ladders lie oppositely across an alley, each with feet at the base of one sidewall, with one leaning against a wall at height
11225:
8982:
Davidov O, Zelen M (2001) Referent sampling, family history and relative risk: the role of length-biased sampling. Biostat 2(2): 173-181
6399:
5452:
9028:
Gurland J (1967) An inequality satisfied by the expectation of the reciprocal of a random variable. The
American Statistician. 21 (2) 24
6912:
The problem of length biased sampling arises in a number of areas including textile manufacture pedigree analysis and survival analysis
4548:
3746:
The same principle applies to more than two segments: given a series of sub-trips at different speeds, if each sub-trip covers the same
2536:
10849:
9490:
9100:
8603:
4355:(true positives per real positive) is often used as an aggregated performance score for the evaluation of algorithms and systems: the
8469:
3912:(48 Ī©): the equivalent resistance, in either case, is 24 Ī© (one-half of the harmonic mean). This same principle applies to
10623:
11062:
2247:
8943:
Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions Vol 1. Wiley Series in
Probability and Statistics.
3874:
to the problem while labeling the mass units by element and making sure that only like element-masses cancel makes this clear.
8657:
8579:
8513:
5692:
9485:
9185:
6546:
5089:
4108:
6193:
5541:
5058:{\displaystyle H_{1-X}={\frac {\beta -1}{\alpha +\beta -1}}{\text{ conditional on }}\beta >1\,\,\&\,\,\alpha >0}
10089:
9237:
8912:
6739:
6334:
8700:
7632:
4703:
9067:
Limbrunner JF, Vogel RM, Brown LC (2000) Estimation of harmonic mean of a lognormal variable. J Hydrol Eng 5(1) 59-66
8617:
Ferger F (1931) The nature and use of the harmonic mean. Journal of the
American Statistical Association 26(173) 36-40
10872:
10764:
9076:
8801:
8725:
6083:
4954:
With the geometric mean the harmonic mean may be useful in maximum likelihood estimation in the four parameter case.
4673:{\displaystyle H={\frac {\alpha -1}{\alpha +\beta -1}}{\text{ conditional on }}\alpha >1\,\,\&\,\,\beta >0}
4535:
3852:
3122:
2046:
6666:
6065:
5794:
4782:
The following are the limits with one parameter finite (non-zero) and the other parameter approaching these limits:
4517:
3834:
3104:
3054:{\displaystyle {\frac {A^{3}}{G^{3}}}+{\frac {G^{3}}{H^{3}}}+1\leq {\frac {3}{4}}\left(1+{\frac {A}{H}}\right)^{2}.}
2028:
11477:
11050:
10924:
5528:
are the parameters of the distribution, i.e. the mean and variance of the distribution of the natural logarithm of
6492:
11108:
10769:
10514:
9885:
9475:
8241:
2425:
11159:
10371:
10178:
10067:
10025:
9113:
EPA (1991) Technical support document for water quality-based toxics control. EPA/505/2-90-001. Office of Water
8537:
6061:
6057:
4513:
4509:
3830:
3826:
3100:
3096:
2024:
2020:
231:
10099:
937:
function, and dominated by the minimum of its arguments, in the sense that for any positive set of arguments,
50:
of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is
11402:
10361:
9264:
6841:
4385:, which is equal to 2.4 hours, to drain the pool together. This is one-half of the harmonic mean of 6 and 4:
4250:
have vertices A, B, C, and D in sequence and have parallel sides AB and CD. Let E be the intersection of the
2483:
2691:, meaning the two numbers' geometric mean equals the geometric mean of their arithmetic and harmonic means.
10953:
10902:
10887:
10877:
10746:
10618:
10585:
10411:
10366:
10196:
8955:
Zelen M (1972) Length-biased sampling and biomedical problems. In: Biometric
Society Meeting, Dallas, Texas
6650:
6318:
2606:
1437:
The arithmetic mean is often mistakenly used in places calling for the harmonic mean. In the speed example
8819:
8627:
5181:
The following are the limits with one parameter finite (non zero) and the other approaching these limits:
11465:
11297:
11098:
11022:
10323:
10077:
9746:
9210:
9019:
Chuen-Teck See, Chen J (2008) Convex functions of random variables. J Inequal Pure Appl Math 9 (3) Art 80
4454:
2119:
3923:
However, if one connects the resistors in series, then the average resistance is the arithmetic mean of
11182:
11154:
11149:
10897:
10656:
10562:
10542:
10450:
10161:
9979:
9462:
9334:
4568:
Harmonic Means for Beta distribution Purple=H(X), Yellow=H(1-X), smaller values alpha and beta in front
9053:
Stedinger JR (1980) Fitting lognormal distributions to hydrologic data. Water Resour Res 16(3) 481ā490
5631:
4576:
Harmonic Means for Beta distribution Purple=H(X), Yellow=H(1-X), larger values alpha and beta in front
10914:
10682:
10403:
10328:
10257:
10186:
10106:
10094:
9964:
9952:
9945:
9653:
9374:
3475:
The unweighted harmonic mean can be regarded as the special case where all of the weights are equal.
2661:
11397:
11164:
11027:
10712:
10677:
10641:
10426:
9868:
9777:
9736:
9648:
9339:
9178:
8550:
8316:
6046:
5615:
4498:
4092:
3966:
3815:
3767:
3085:
2009:
8998:
Zelen M, Feinleib M (1969) On the theory of screening for chronic diseases. Biometrika 56: 601-614
11306:
10919:
10859:
10796:
10434:
10418:
10156:
10018:
10008:
9858:
9772:
8311:
7034:{\displaystyle \operatorname {Var} \left<\operatorname {Var} \left({\frac {1}{X^{q}}}\right).}
6050:
4502:
4277:
3819:
3089:
2013:
9037:
Sung SH (2010) On inverse moments for a class of nonnegative random variables. J Inequal Applic
8793:
11344:
11274:
11067:
11004:
10759:
10646:
9643:
9540:
9447:
9326:
9225:
8367:
7132:
5439:
4424:
4412:
1982:
43:
8770:
11369:
11311:
11254:
11080:
10973:
10882:
10608:
10492:
10351:
10343:
10233:
10225:
10040:
9936:
9914:
9873:
9838:
9805:
9751:
9726:
9681:
9620:
9580:
9382:
9205:
8934:
Rossman LA (1990) Design stream flows based on harmonic means. J Hydr Eng ASCE 116(7) 946ā950
8321:
8248:
6097:
4340:
1052:{\displaystyle \min(x_{1}\ldots x_{n})\leq H(x_{1}\ldots x_{n})\leq n\min(x_{1}\ldots x_{n})}
9154:
4359:(or F-measure). This is used in information retrieval because only the positive class is of
11292:
10867:
10816:
10792:
10754:
10672:
10651:
10603:
10482:
10460:
10429:
10338:
10215:
10166:
10084:
10057:
10013:
9969:
9731:
9507:
9387:
4352:
4348:
4127:
3871:
3222:
3195:
3168:
3141:
2756:
2729:
2702:
2217:
2190:
9122:
Muskat M (1937) The flow of homogeneous fluids through porous media. McGraw-Hill, New York
8964:
Lam FC (1985) Estimate of variance for harmonic mean half lives. J Pharm Sci 74(2) 229-231
8466:
8:
11439:
11364:
11287:
10968:
10732:
10725:
10687:
10595:
10575:
10547:
10280:
10146:
10141:
10131:
10123:
9941:
9902:
9792:
9782:
9691:
9470:
9426:
9344:
9269:
9171:
8565:
8276:
6619:
5683:
4439:
4170:
4112:
4091:
The weighted harmonic mean is the preferable method for averaging multiples, such as the
3883:
2931:
are respectively the harmonic, geometric, and arithmetic means of three positive numbers
1083:
7342:{\displaystyle \operatorname {E} (a+X)^{-n}\sim \operatorname {E} \left(a+X^{-n}\right)}
5996:{\displaystyle \operatorname {Var} \left({\frac {1}{x}}\right)={\frac {m\left}{nm^{2}}}}
4304:. This result still holds if the walls are slanted but still parallel and the "heights"
11453:
11264:
11118:
11014:
10963:
10839:
10736:
10720:
10697:
10474:
10208:
10191:
10151:
10062:
9957:
9919:
9890:
9850:
9810:
9756:
9673:
9359:
9354:
8786:
8758:
8301:
8291:
8268:
4450:
limiting the genetic variation present in the population for many generations to come.
3494:
36:
4138:
from B and C respectively, and with the intersection of PA and BC being at a distance
2158:
1078:
11448:
11359:
11329:
11321:
11141:
11132:
11057:
10988:
10844:
10829:
10804:
10692:
10633:
10499:
10487:
10113:
10030:
9974:
9897:
9741:
9663:
9442:
9316:
9137:
9094:
8797:
8766:
8750:
8721:
8696:
8597:
8533:
8391:
8262:
6831:
The expectation of the harmonic mean is the same as the non-length biased version E(
4581:
4324:
2069:
1063:
by changing some values to bigger ones (while having at least one value unchanged).
1060:
32:
8987:
7364:) are drawn from a lognormal distribution there are several possible estimators for
11384:
11339:
11103:
11090:
10983:
10958:
10892:
10824:
10702:
10310:
10203:
10136:
10049:
9996:
9815:
9686:
9480:
9364:
9279:
9246:
9038:
8983:
8281:
7138:
Gurland has shown that for a distribution that takes only positive values, for any
4462:(the federal automobile fuel consumption standards) make use of the harmonic mean.
4344:
4336:
1103:
1067:
9140:
8665:
8572:
8244:
recommends the use of the harmonic mean in setting maximum toxin levels in water.
4443:
1190:, the harmonic mean is always the least of the three Pythagorean means, while the
11301:
11045:
10907:
10834:
10509:
10383:
10356:
10333:
10302:
9929:
9924:
9878:
9608:
9259:
8517:
8510:
8473:
8286:
4470:
3784:
3672:
3136:
2420:
2085:
1191:
1125:
490:
47:
10791:
11499:
11250:
11245:
9708:
9638:
9284:
8692:
8306:
5761:
4459:
4158:
4119:
3962:
3754:
mean of all the sub-trip speeds; and if each sub-trip takes the same amount of
2932:
2909:{\displaystyle H={\frac {3x_{1}x_{2}x_{3}}{x_{1}x_{2}+x_{1}x_{3}+x_{2}x_{3}}}.}
2478:
2113:
2105:
2093:
1464:, which goes with the arithmetic mean, is the geometric mean to the power
1195:
1136:
1114:
8906:
8380:
Using
Pythagoras' theorem, OC² = OG² + GC² ∴ GC = √
7121:{\displaystyle \operatorname {E} \left\geq {\frac {1}{\operatorname {E} (X)}}}
924:{\textstyle A(x_{1},x_{2},\ldots ,x_{n})={\tfrac {1}{n}}\sum _{i=1}^{n}x_{i}.}
11493:
11407:
11374:
11237:
11198:
11009:
10978:
10442:
10396:
10001:
9703:
9530:
9294:
8754:
8296:
4560:(Mean - HarmonicMean) for Beta distribution versus alpha and beta from 0 to 2
4059:
934:
6169:{\displaystyle \operatorname {Var} (H)={\frac {1}{n}}{\frac {s^{2}}{m^{4}}}}
11349:
11282:
11259:
11174:
10504:
9800:
9698:
9633:
9575:
9560:
9497:
9452:
9158:
6101:
4552:
Harmonic mean for Beta distribution for 0 < Ī± < 5 and 0 < Ī² < 5
4420:
4218:
4123:
9042:
11392:
11354:
11037:
10938:
10800:
10613:
10580:
10072:
9989:
9984:
9628:
9585:
9565:
9545:
9535:
9304:
6919:
have developed a test for the detection of length based bias in samples.
4432:
226:
20:
8762:
7769:{\displaystyle s^{2}={\frac {1}{n}}\sum \left(\log _{e}(x)-m\right)^{2}}
5760:
For a random sample, the harmonic mean is calculated as above. Both the
5072:< 1 is undefined because its defining expression is not bounded in .
4687:< 1 is undefined because its defining expression is not bounded in .
10238:
9718:
9418:
9349:
9299:
9274:
9194:
4177:
2409:{\displaystyle \qquad {\frac {1}{H}}={\frac {(1/x_{1})+(1/x_{2})}{2}}.}
2109:
1210:
6324:
This method first requires the computation of the mean of the sample (
10391:
10243:
9863:
9658:
9570:
9555:
9550:
9515:
9145:
8718:
The Handbook of Business Valuation and Intellectual Property Analysis
6295:{\displaystyle s^{2}=\operatorname {Var} \left({\frac {1}{x}}\right)}
5535:
The harmonic and arithmetic means of the distribution are related by
4466:
4447:
4408:
4360:
4247:
3940:
3913:
6035:
5625:), arithmetic and harmonic means of the distribution are related by
4487:
3804:
3074:
2064:
1998:
9907:
9525:
9402:
9397:
9392:
6465:{\displaystyle w_{i}={\frac {n-1}{\sum _{j\neq i}{\frac {1}{x}}}}.}
5769:
5765:
5510:{\displaystyle H=\exp \left(\mu -{\frac {1}{2}}\sigma ^{2}\right),}
4428:
4356:
4251:
4104:
3944:
3931:(50 Ī©), with total resistance equal to twice this, the sum of
3917:
3889:
2175:
1460:
numbers except the second; and so on. The numerator, excluding the
1441:
for instance, the arithmetic mean of 40 is incorrect, and too big.
8548:
Mitchell, Douglas W., "More on spreads and non-arithmetic means,"
7963:
Similarly a first order approximation to the bias and variance of
2593:{\displaystyle H={\frac {G^{2}}{A}}=G\left({\frac {G}{A}}\right).}
11412:
11113:
8486:
4320:
4257:
4026:
is one-half of the harmonic mean of the distances of the subject
3762:
mean of all the sub-trip speeds. (If neither is the case, then a
3502:
28:
11334:
10315:
10289:
10269:
9520:
9311:
6623:
3517:(e.g. 20 km/h), then its average speed is the harmonic mean of
8628:"Average: How to calculate Average, Formula, Weighted average"
35:. It is sometimes appropriate for situations when the average
9163:
3866:
3498:
8891:
Richinick, Jennifer, "The upside-down Pythagorean Theorem,"
8211:
is generally a superior estimator of the harmonic mean than
5775:
4076:
in series is equivalent to two thin lenses of optical power
9254:
7795:
4051:
in series is equivalent to two thin lenses of focal length
2315:{\displaystyle H={\frac {2x_{1}x_{2}}{x_{1}+x_{2}}}\qquad }
1476:-th geometric and arithmetic means. The general formula is
8740:
7786:
is probably the best estimator for samples of 25 or more.
4284:
and the other leaning against the opposite wall at height
2419:
In this special case, the harmonic mean is related to the
1456:
numbers except the first; for the second, we multiply all
16:
Inverse of the average of the inverses of a set of numbers
3897:
6096:
Assuming that the variance is not infinite and that the
3659:
However, if the vehicle travels for a certain amount of
3513:(e.g. 60 km/h) and returns the same distance at a speed
3505:. For instance, if a vehicle travels a certain distance
1988:
3865:
Similarly, if one wishes to estimate the density of an
1452:-th term. That is, for the first term, we multiply all
9135:
6729:
The expectation of this length biased distribution E(
5784:
is asymptotically distributed normally with variance
5734:{\displaystyle H=k\left(1+{\frac {1}{\alpha }}\right)}
2611:
876:
820:
8822:
8370:, QC² = QO² + OC² ∴ QC = √
7979:
7814:
7694:
7635:
7377:
7269:
7151:
7066:
6948:
6844:
6742:
6669:
6608:{\displaystyle {\frac {n-1}{n}}\sum {(m-w_{i})}^{2}.}
6549:
6495:
6402:
6337:
6254:
6196:
6113:
5899:
5797:
5695:
5634:
5544:
5455:
5190:
5144:{\displaystyle H_{1-X}={\frac {\beta -1}{2\beta -1}}}
5092:
4973:
4791:
4706:
4601:
3259:
3225:
3198:
3171:
3144:
2944:
2789:
2759:
2732:
2705:
2664:
2609:
2539:
2486:
2428:
2328:
2250:
2220:
2193:
2122:
1482:
1219:
943:
717:
570:
502:
431:
356:
296:
234:
59:
11076:
Autoregressive conditional heteroskedasticity (ARCH)
8784:
Posamentier, Alfred S.; Salkind, Charles T. (1996).
8258:
6232:{\displaystyle m={\frac {1}{n}}\sum {\frac {1}{x}}.}
5772:(if it includes at least one term of the form 1/0).
5593:{\displaystyle {\frac {\mu ^{*}}{H}}=1+C_{v}^{2}\,,}
1981:
If a set of non-identical numbers is subjected to a
6814:{\displaystyle \operatorname {E} ^{*}(x)=\mu \left}
4276:One application of this trapezoid result is in the
10538:
8870:
8785:
8783:
8716:"Fairness Opinions: Common Errors and Omissions".
8193:
7942:
7768:
7679:
7615:
7341:
7249:
7120:
7033:
6901:
6813:
6718:
6607:
6529:
6464:
6369:{\displaystyle m={\frac {n}{\sum {\frac {1}{x}}}}}
6368:
6294:
6231:
6168:
5995:
5879:
5733:
5666:
5592:
5509:
5418:Although both harmonic means are asymmetric, when
5407:
5143:
5057:
4943:
4744:
4672:
3464:
3238:
3211:
3184:
3157:
3053:
2908:
2772:
2745:
2718:
2683:
2630:
2592:
2522:
2469:
2408:
2314:
2233:
2206:
2146:
1971:
1423:
1051:
923:
803:
478:
279:
205:
9063:
9061:
9059:
9015:
9013:
7680:{\displaystyle m={\frac {1}{n}}\sum \log _{e}(x)}
4745:{\displaystyle H={\frac {\alpha -1}{2\alpha -1}}}
4411:, the harmonic mean is similarly used to average
2162:A graphical interpretation of the harmonic mean,
11491:
5618:and the mean of the distribution respectively..
5364:
5325:
5283:
5244:
5196:
4913:
4887:
4858:
4832:
4797:
4351:(true positives per predicted positive) and the
1073:
1017:
944:
10624:Multivariate adaptive regression splines (MARS)
8225:produces estimates that are largely similar to
7789:
6245:is the variance of the reciprocals of the data
4058:, their harmonic mean, in series. Expressed as
1188:containing at least one pair of nonequal values
9056:
9010:
8904:
8511:http://ajmaa.org/RGMIA/papers/v2n1/v2n1-10.pdf
6719:{\displaystyle f^{*}(x)={\frac {xf(x)}{\mu }}}
5880:{\displaystyle s^{2}={\frac {m\left}{m^{2}n}}}
9179:
9047:
8919:
4288:, as shown. The ladders cross at a height of
8951:
8949:
6622:for the mean can then be estimated with the
6530:{\displaystyle h={\frac {1}{n}}\sum {w_{i}}}
6309:is the number of data points in the sample.
4022:can be rewritten such that the focal length
3667:and then the same amount of time at a speed
2640:inequality of arithmetic and geometric means
1194:is always the greatest of the three and the
9022:
8976:
8937:
8928:
8251:studies, the harmonic mean is widely used.
6634:Assume a random variate has a distribution
6064:. Unsourced material may be challenged and
6010:is the arithmetic mean of the reciprocals,
4516:. Unsourced material may be challenged and
3833:. Unsourced material may be challenged and
3763:
3103:. Unsourced material may be challenged and
2027:. Unsourced material may be challenged and
9224:
9186:
9172:
9116:
6187:is the arithmetic mean of the reciprocals
3683:, which in the above example is 40 km/h.
2470:{\displaystyle A={\frac {x_{1}+x_{2}}{2}}}
2187:For the special case of just two numbers,
42:The harmonic mean can be expressed as the
9837:
9001:
8992:
8946:
8611:
8532:, Ya-lun Chou, Holt International, 1969,
6084:Learn how and when to remove this message
5776:Sample distributions of mean and variance
5586:
5429:
5045:
5044:
5040:
5039:
4660:
4659:
4655:
4654:
4536:Learn how and when to remove this message
4111:is one-third of the harmonic mean of the
3853:Learn how and when to remove this message
3501:, the harmonic mean provides the correct
3123:Learn how and when to remove this message
3064:
2047:Learn how and when to remove this message
1059:. Thus, the harmonic mean cannot be made
280:{\displaystyle x_{1},x_{2},\ldots ,x_{n}}
199:
9031:
6649:be the mean of the population. Then the
4571:
4563:
4555:
4547:
4256:
3939:(100 Ī©). This principle applies to
2157:
2063:
1077:
814:where the arithmetic mean is defined as
9155:Averages, Arithmetic and Harmonic Means
9107:
8967:
8958:
6902:{\displaystyle E^{*}(x^{-1})=E(x)^{-1}}
6629:
3686:Average speed for the entire journey =
3528:Average speed for the entire journey =
2699:For the special case of three numbers,
2654:(a property that in fact holds for all
2523:{\displaystyle G={\sqrt {x_{1}x_{2}}},}
11492:
11150:KaplanāMeier estimator (product limit)
9099:: CS1 maint: archived copy as title (
8680:
8602:: CS1 maint: archived copy as title (
7355:
7352:where ~ means approximately equal to.
5677:
2068:A geometric construction of the three
11223:
10790:
10537:
9836:
9606:
9223:
9167:
9136:
8686:
8638:from the original on 29 December 2017
8484:
6100:applies to the sample then using the
5162:the harmonic mean ranges from 0, for
4219:inscribed squares in a right triangle
2631:{\displaystyle {\tfrac {G}{A}}\leq 1}
1989:Harmonic mean of two or three numbers
11460:
11160:Accelerated failure time (AFT) model
8871:{\displaystyle a^{-2}+b^{-2}=d^{-2}}
8816:Voles, Roger, "Integer solutions of
6922:
6062:adding citations to reliable sources
6029:
4964:) also exists for this distribution
4763:the harmonic mean ranges from 0 for
4514:adding citations to reliable sources
4481:
4477:
4330:
4083:, their arithmetic mean, in series.
4062:, two thin lenses of optical powers
3831:adding citations to reliable sources
3798:
3101:adding citations to reliable sources
3068:
2025:adding citations to reliable sources
1992:
1472:-th harmonic mean is related to the
493:of the reciprocals, and vice versa:
11472:
10755:Analysis of variance (ANOVA, anova)
9607:
8557:
7794:A first order approximation to the
6660:) of the size biased population is
6312:
5890:The variance of the mean itself is
3892:in parallel, one having resistance
3775:each trip segment i, the slowness s
3413:
3362:
3303:
3270:
2780:, the harmonic mean can be written
2241:, the harmonic mean can be written
2147:{\displaystyle H\leq G\leq A\leq Q}
1927:
1868:
1815:
13:
10850:CochranāMantelāHaenszel statistics
9476:Pearson product-moment correlation
8792:(Second ed.). Dover. p.
8658:"Effective mass in semiconductors"
7304:
7270:
7217:
7185:
7152:
7100:
7067:
6931:is a positive random variable and
6744:
5938:
5822:
5374:
5293:
5041:
4923:
4868:
4656:
2080:. The harmonic mean is denoted by
14:
11511:
9129:
8478:
7960:is the coefficient of variation.
4231:equals half the harmonic mean of
2112:is always longer than a leg of a
1448:times but each time omitting the
1171:of two distinct positive numbers
11471:
11459:
11447:
11434:
11433:
11224:
8915:from the original on 2005-04-06.
8788:Challenging Problems in Geometry
8261:
6034:
5667:{\displaystyle H\mu ^{*}=G^{2}.}
4486:
4037:Two thin lenses of focal length
3803:
3758:, then the average speed is the
3750:, then the average speed is the
3671:, then its average speed is the
3488:
3073:
2694:
1997:
31:, and in particular, one of the
11109:Least-squares spectral analysis
8898:
8885:
8810:
8777:
8734:
8709:
8650:
8585:from the original on 2014-10-15
8242:Environmental Protection Agency
6025:
3888:If one connects two electrical
2935:the following inequality holds
2329:
2311:
10090:Mean-unbiased minimum-variance
9193:
8905:Van Rijsbergen, C. J. (1979).
8743:Journal of Financial Education
8620:
8542:
8522:
8503:
8460:
8334:
7746:
7740:
7674:
7668:
7540:
7534:
7501:
7495:
7289:
7276:
7112:
7106:
6978:
6965:
6887:
6880:
6871:
6855:
6762:
6756:
6707:
6701:
6686:
6680:
6592:
6573:
6126:
6120:
5371:
5332:
5290:
5251:
5203:
4920:
4894:
4865:
4839:
4804:
4427:is the harmonic mean of their
4098:
3877:
3192:is associated to the data set
2684:{\displaystyle G={\sqrt {AH}}}
2394:
2373:
2367:
2346:
2059:
1046:
1020:
1008:
982:
973:
947:
869:
824:
702:
657:
555:
510:
345:
300:
1:
11403:Geographic information system
10619:Simultaneous equations models
8988:10.1093/biostatistics/2.2.173
8911:(2nd ed.). Butterworth.
8453:
6022:is the expectation operator.
5755:
4296:is half the harmonic mean of
4265:is half the harmonic mean of
4186:is half the harmonic mean of
4146:is half the harmonic mean of
4086:
3493:In many situations involving
3483:
1438:
1074:Relationship with other means
216:
10586:Coefficient of determination
10197:Uniformly most powerful test
7790:Bias and variance estimators
7360:Assuming that the variates (
6651:probability density function
6540:The variance of the mean is
5682:The harmonic mean of type 1
4292:above the alley floor. Then
3900:) and one having resistance
3698:Sum of time for each segment
3540:Sum of time for each segment
489:It is the reciprocal of the
7:
11155:Proportional hazards models
11099:Spectral density estimation
11081:Vector autoregression (VAR)
10515:Maximum posterior estimator
9747:Randomized controlled trial
8254:
6018:is the population size and
5748:is the scale parameter and
4455:fuel economy in automobiles
4347:, the harmonic mean of the
4142:from point P, we have that
3478:
2104:denotes a fourth mean, the
27:is one of several kinds of
10:
11516:
10915:Multivariate distributions
9335:Average absolute deviation
8564:Inequalities proposed in "
8327:
7044:
5027: conditional on
4642: conditional on
4217:) be the sides of the two
3881:
3794:
1066:The harmonic mean is also
11429:
11383:
11320:
11273:
11236:
11232:
11219:
11191:
11173:
11140:
11131:
11089:
11036:
10997:
10946:
10937:
10903:Structural equation model
10858:
10815:
10811:
10786:
10745:
10711:
10665:
10632:
10594:
10561:
10557:
10533:
10473:
10382:
10301:
10265:
10256:
10239:Score/Lagrange multiplier
10224:
10177:
10122:
10048:
10039:
9849:
9845:
9832:
9791:
9765:
9717:
9672:
9654:Sample size determination
9619:
9615:
9602:
9506:
9461:
9435:
9417:
9373:
9325:
9245:
9236:
9232:
9219:
9201:
8382:OC² − OG²
8204:In numerical experiments
6618:Significance testing and
5426:the two means are equal.
3956:
3783:. Then take the weighted
2116:, the diagram shows that
11398:Environmental statistics
10920:Elliptical distributions
10713:Generalized linear model
10642:Simple linear regression
10412:HodgesāLehmann estimator
9869:Probability distribution
9778:Stochastic approximation
9340:Coefficient of variation
8895:92, July 2008, 313ā;317.
8554:88, March 2004, 142ā144.
8551:The Mathematical Gazette
8317:HM-GM-AM-QM inequalities
8235:
5752:is the shape parameter.
5616:coefficient of variation
5083:in the above expression
5068:This harmonic mean with
4957:A second harmonic mean (
3768:weighted arithmetic mean
2658:). It also follows that
11058:Cross-correlation (XCF)
10666:Non-standard predictors
10100:LehmannāScheffĆ© theorem
9773:Adaptive clinical trial
8882:83, July 1999, 269ā271.
8312:Weighted geometric mean
6393:is then computed where
6383:are the sample values.
5780:The mean of the sample
4683:The harmonic mean with
4580:The harmonic mean of a
4278:crossed ladders problem
4118:For any point P on the
3692:Total distance traveled
3534:Total distance traveled
2919:Three positive numbers
1202:It is the special case
933:The harmonic mean is a
11454:Mathematics portal
11275:Engineering statistics
11183:NelsonāAalen estimator
10760:Analysis of covariance
10647:Ordinary least squares
10571:Pearson product-moment
9975:Statistical functional
9886:Empirical distribution
9719:Controlled experiments
9448:Frequency distribution
9226:Descriptive statistics
8872:
8687:Hecht, Eugene (2002).
8195:
7944:
7770:
7681:
7617:
7343:
7260:Under some conditions
7251:
7122:
7035:
6903:
6815:
6720:
6609:
6531:
6466:
6370:
6296:
6233:
6183:is the harmonic mean,
6170:
5997:
5881:
5735:
5668:
5594:
5511:
5440:lognormal distribution
5430:Lognormal distribution
5409:
5145:
5059:
4945:
4746:
4674:
4584:with shape parameters
4577:
4569:
4561:
4553:
4423:, a baseball player's
4413:hydraulic conductivity
4273:
3764:weighted harmonic mean
3466:
3432:
3381:
3322:
3289:
3248:weighted harmonic mean
3240:
3213:
3186:
3159:
3065:Weighted harmonic mean
3055:
2910:
2774:
2747:
2720:
2685:
2632:
2594:
2524:
2471:
2410:
2316:
2235:
2208:
2184:
2155:
2148:
1983:mean-preserving spread
1973:
1946:
1887:
1834:
1425:
1179:
1053:
925:
907:
805:
480:
452:
281:
207:
11370:Population statistics
11312:System identification
11046:Autocorrelation (ACF)
10974:Exponential smoothing
10888:Discriminant analysis
10883:Canonical correlation
10747:Partition of variance
10609:Regression validation
10453:(JonckheereāTerpstra)
10352:Likelihood-ratio test
10041:Frequentist inference
9953:Locationāscale family
9874:Sampling distribution
9839:Statistical inference
9806:Cross-sectional study
9793:Observational studies
9752:Randomized experiment
9581:Stem-and-leaf display
9383:Central limit theorem
8908:Information Retrieval
8873:
8720:. McGraw Hill. 2004.
8491:mathworld.wolfram.com
8322:Harmonic mean p-value
8249:reservoir engineering
8196:
7945:
7771:
7682:
7618:
7344:
7252:
7123:
7036:
6904:
6816:
6721:
6610:
6532:
6467:
6371:
6297:
6234:
6171:
6098:central limit theorem
5998:
5882:
5736:
5669:
5595:
5512:
5442:of a random variable
5410:
5236: undefined
5146:
5060:
4946:
4824: undefined
4747:
4675:
4575:
4567:
4559:
4551:
4341:information retrieval
4260:
3467:
3412:
3361:
3302:
3269:
3241:
3239:{\displaystyle x_{n}}
3214:
3212:{\displaystyle x_{1}}
3187:
3185:{\displaystyle w_{n}}
3160:
3158:{\displaystyle w_{1}}
3056:
2911:
2775:
2773:{\displaystyle x_{3}}
2748:
2746:{\displaystyle x_{2}}
2721:
2719:{\displaystyle x_{1}}
2686:
2642:, this shows for the
2633:
2595:
2525:
2472:
2411:
2317:
2236:
2234:{\displaystyle x_{2}}
2209:
2207:{\displaystyle x_{1}}
2161:
2149:
2084:in purple, while the
2067:
1974:
1926:
1867:
1814:
1426:
1081:
1054:
926:
887:
806:
481:
432:
282:
208:
11293:Probabilistic design
10878:Principal components
10721:Exponential families
10673:Nonlinear regression
10652:General linear model
10614:Mixed effects models
10604:Errors and residuals
10581:Confounding variable
10483:Bayesian probability
10461:Van der Waerden test
10451:Ordered alternative
10216:Multiple comparisons
10095:RaoāBlackwellization
10058:Estimating equations
10014:Statistical distance
9732:Factorial experiment
9265:Arithmetic-Geometric
8893:Mathematical Gazette
8880:Mathematical Gazette
8820:
8530:Statistical Analysis
7977:
7812:
7692:
7633:
7375:
7267:
7149:
7064:
6946:
6935:> 0 then for all
6842:
6740:
6667:
6630:Size biased sampling
6620:confidence intervals
6547:
6493:
6400:
6335:
6252:
6194:
6111:
6058:improve this section
5897:
5795:
5693:
5632:
5542:
5453:
5434:The harmonic mean (
5188:
5090:
4971:
4789:
4704:
4599:
4510:improve this section
4180:to the right angle,
4130:ABC, with distances
4128:equilateral triangle
4107:, the radius of the
4093:priceāearnings ratio
3872:dimensional analysis
3827:improve this section
3509:outbound at a speed
3257:
3223:
3196:
3169:
3142:
3097:improve this section
2942:
2787:
2757:
2730:
2703:
2662:
2607:
2537:
2484:
2426:
2326:
2248:
2218:
2191:
2120:
2021:improve this section
1480:
1217:
941:
818:
500:
294:
232:
57:
11365:Official statistics
11288:Methods engineering
10969:Seasonal adjustment
10737:Poisson regressions
10657:Bayesian regression
10596:Regression analysis
10576:Partial correlation
10548:Regression analysis
10147:Prediction interval
10142:Likelihood interval
10132:Confidence interval
10124:Interval estimation
10085:Unbiased estimators
9903:Model specification
9783:Up-and-down designs
9471:Partial correlation
9427:Index of dispersion
9345:Interquartile range
9043:10.1155/2010/823767
8632:learningpundits.com
8566:Crux Mathematicorum
8485:Weisstein, Eric W.
8372:QO² + OC²
8368:Pythagoras' theorem
8277:Contraharmonic mean
8175:
8074:
7356:Sampling properties
7133:Jensen's inequality
5684:Pareto distribution
5678:Pareto distribution
5585:
4440:population genetics
3884:Parallel (operator)
3409:
1417:
1390:
1369:
1084:proof without words
11385:Spatial statistics
11265:Medical statistics
11165:First hitting time
11119:Whittle likelihood
10770:Degrees of freedom
10765:Multivariate ANOVA
10698:Heteroscedasticity
10510:Bayesian estimator
10475:Bayesian inference
10324:KolmogorovāSmirnov
10209:Randomization test
10179:Testing hypotheses
10152:Tolerance interval
10063:Maximum likelihood
9958:Exponential family
9891:Density estimation
9851:Statistical theory
9811:Natural experiment
9757:Scientific control
9674:Survey methodology
9360:Standard deviation
9138:Weisstein, Eric W.
8868:
8668:on 20 October 2017
8516:2015-12-22 at the
8472:2022-07-11 at the
8302:Parallel summation
8292:Rate (mathematics)
8269:Mathematics portal
8191:
8189:
8161:
8060:
7940:
7938:
7766:
7677:
7613:
7611:
7339:
7247:
7131:This follows from
7118:
7057:) are > 0 then
7031:
6899:
6811:
6716:
6605:
6527:
6462:
6445:
6386:A series of value
6366:
6292:
6229:
6166:
6104:, the variance is
6014:are the variates,
5993:
5877:
5731:
5664:
5590:
5571:
5507:
5405:
5403:
5378:
5339:
5297:
5258:
5210:
5141:
5055:
4941:
4939:
4927:
4901:
4872:
4846:
4811:
4742:
4670:
4578:
4570:
4562:
4554:
4425:Powerāspeed number
4274:
3967:thin lens equation
3943:in parallel or to
3462:
3392:
3236:
3209:
3182:
3155:
3051:
2906:
2770:
2743:
2716:
2681:
2628:
2620:
2590:
2520:
2467:
2406:
2312:
2231:
2204:
2185:
2156:
2144:
1969:
1421:
1400:
1373:
1352:
1180:
1049:
921:
885:
801:
799:
791:
644:
476:
470:
420:
277:
221:The harmonic mean
203:
11487:
11486:
11425:
11424:
11421:
11420:
11360:National accounts
11330:Actuarial science
11322:Social statistics
11215:
11214:
11211:
11210:
11207:
11206:
11142:Survival function
11127:
11126:
10989:Granger causality
10830:Contingency table
10805:Survival analysis
10782:
10781:
10778:
10777:
10634:Linear regression
10529:
10528:
10525:
10524:
10500:Credible interval
10469:
10468:
10252:
10251:
10068:Method of moments
9937:Parametric family
9898:Statistical model
9828:
9827:
9824:
9823:
9742:Random assignment
9664:Statistical power
9598:
9597:
9594:
9593:
9443:Contingency table
9413:
9412:
9280:Generalized/power
8662:ecee.colorado.edu
8392:similar triangles
8180:
8139:
8079:
8038:
7934:
7870:
7716:
7650:
7592:
7544:
7529:
7477:
7427:
7420:
7242:
7116:
7085:
7022:
6988:
6923:Shifted variables
6828:is the variance.
6804:
6714:
6566:
6510:
6457:
6454:
6430:
6364:
6361:
6286:
6224:
6211:
6164:
6140:
6094:
6093:
6086:
5991:
5957:
5918:
5875:
5841:
5724:
5560:
5487:
5363:
5324:
5282:
5243:
5237:
5195:
5170:= 1, to 1/2, for
5154:showing that for
5139:
5028:
5023:
4912:
4886:
4857:
4831:
4825:
4796:
4755:showing that for
4740:
4643:
4638:
4582:beta distribution
4546:
4545:
4538:
4478:Beta distribution
4453:When considering
4331:In other sciences
4325:semi-latus rectum
4261:Crossed ladders.
3863:
3862:
3855:
3444:
3348:
3345:
3133:
3132:
3125:
3035:
3013:
2994:
2967:
2901:
2679:
2619:
2581:
2561:
2515:
2465:
2401:
2338:
2309:
2070:Pythagorean means
2057:
2056:
2049:
1964:
1923:
1864:
1811:
1721:
1419:
1061:arbitrarily large
884:
792:
784:
761:
741:
645:
637:
614:
594:
471:
468:
421:
418:
392:
372:
287:is defined to be
191:
178:
175:
162:
149:
117:
33:Pythagorean means
11507:
11475:
11474:
11463:
11462:
11452:
11451:
11437:
11436:
11340:Crime statistics
11234:
11233:
11221:
11220:
11138:
11137:
11104:Fourier analysis
11091:Frequency domain
11071:
11018:
10984:Structural break
10944:
10943:
10893:Cluster analysis
10840:Log-linear model
10813:
10812:
10788:
10787:
10729:
10703:Homoscedasticity
10559:
10558:
10535:
10534:
10454:
10446:
10438:
10437:(KruskalāWallis)
10422:
10407:
10362:Cross validation
10347:
10329:AndersonāDarling
10276:
10263:
10262:
10234:Likelihood-ratio
10226:Parametric tests
10204:Permutation test
10187:1- & 2-tails
10078:Minimum distance
10050:Point estimation
10046:
10045:
9997:Optimal decision
9948:
9847:
9846:
9834:
9833:
9816:Quasi-experiment
9766:Adaptive designs
9617:
9616:
9604:
9603:
9481:Rank correlation
9243:
9242:
9234:
9233:
9221:
9220:
9188:
9181:
9174:
9165:
9164:
9151:
9150:
9123:
9120:
9114:
9111:
9105:
9104:
9098:
9090:
9088:
9087:
9081:
9075:. Archived from
9074:
9065:
9054:
9051:
9045:
9035:
9029:
9026:
9020:
9017:
9008:
9005:
8999:
8996:
8990:
8980:
8974:
8971:
8965:
8962:
8956:
8953:
8944:
8941:
8935:
8932:
8926:
8923:
8917:
8916:
8902:
8896:
8889:
8883:
8877:
8875:
8874:
8869:
8867:
8866:
8851:
8850:
8835:
8834:
8814:
8808:
8807:
8791:
8781:
8775:
8774:
8738:
8732:
8731:
8713:
8707:
8706:
8691:(4th ed.).
8684:
8678:
8677:
8675:
8673:
8664:. Archived from
8654:
8648:
8647:
8645:
8643:
8624:
8618:
8615:
8609:
8607:
8601:
8593:
8591:
8590:
8584:
8577:
8561:
8555:
8546:
8540:
8526:
8520:
8507:
8501:
8500:
8498:
8497:
8482:
8476:
8464:
8447:
8441:
8439:
8438:
8435:
8432:
8425:
8423:
8422:
8419:
8416:
8409:
8407:
8406:
8403:
8400:
8383:
8373:
8338:
8282:Generalized mean
8271:
8266:
8265:
8200:
8198:
8197:
8192:
8190:
8186:
8182:
8181:
8176:
8174:
8169:
8153:
8140:
8135:
8134:
8130:
8129:
8128:
8105:
8104:
8091:
8085:
8081:
8080:
8075:
8073:
8068:
8052:
8039:
8037:
8029:
8028:
8024:
8023:
8022:
7999:
7998:
7985:
7949:
7947:
7946:
7941:
7939:
7935:
7930:
7929:
7928:
7919:
7918:
7908:
7899:
7895:
7894:
7871:
7866:
7865:
7864:
7851:
7842:
7838:
7837:
7798:and variance of
7775:
7773:
7772:
7767:
7765:
7764:
7759:
7755:
7736:
7735:
7717:
7709:
7704:
7703:
7686:
7684:
7683:
7678:
7664:
7663:
7651:
7643:
7622:
7620:
7619:
7614:
7612:
7608:
7604:
7603:
7602:
7593:
7585:
7559:
7558:
7545:
7543:
7530:
7522:
7519:
7518:
7513:
7509:
7508:
7504:
7491:
7490:
7478:
7470:
7451:
7442:
7441:
7428:
7426:
7425:
7421:
7413:
7400:
7391:
7390:
7348:
7346:
7345:
7340:
7338:
7334:
7333:
7332:
7300:
7299:
7256:
7254:
7253:
7248:
7243:
7241:
7240:
7236:
7235:
7215:
7214:
7210:
7209:
7183:
7178:
7174:
7173:
7127:
7125:
7124:
7119:
7117:
7115:
7095:
7090:
7086:
7078:
7040:
7038:
7037:
7032:
7027:
7023:
7021:
7020:
7008:
6993:
6989:
6987:
6986:
6985:
6960:
6908:
6906:
6905:
6900:
6898:
6897:
6870:
6869:
6854:
6853:
6820:
6818:
6817:
6812:
6810:
6806:
6805:
6803:
6802:
6793:
6792:
6783:
6752:
6751:
6725:
6723:
6722:
6717:
6715:
6710:
6693:
6679:
6678:
6614:
6612:
6611:
6606:
6601:
6600:
6595:
6591:
6590:
6567:
6562:
6551:
6536:
6534:
6533:
6528:
6526:
6525:
6524:
6511:
6503:
6471:
6469:
6468:
6463:
6458:
6456:
6455:
6447:
6444:
6428:
6417:
6412:
6411:
6375:
6373:
6372:
6367:
6365:
6363:
6362:
6354:
6345:
6313:Jackknife method
6301:
6299:
6298:
6293:
6291:
6287:
6279:
6264:
6263:
6238:
6236:
6235:
6230:
6225:
6217:
6212:
6204:
6175:
6173:
6172:
6167:
6165:
6163:
6162:
6153:
6152:
6143:
6141:
6133:
6089:
6082:
6078:
6075:
6069:
6038:
6030:
6002:
6000:
5999:
5994:
5992:
5990:
5989:
5988:
5975:
5974:
5970:
5969:
5965:
5958:
5950:
5928:
5923:
5919:
5911:
5886:
5884:
5883:
5878:
5876:
5874:
5870:
5869:
5859:
5858:
5854:
5853:
5849:
5842:
5834:
5812:
5807:
5806:
5740:
5738:
5737:
5732:
5730:
5726:
5725:
5717:
5673:
5671:
5670:
5665:
5660:
5659:
5647:
5646:
5599:
5597:
5596:
5591:
5584:
5579:
5561:
5556:
5555:
5546:
5516:
5514:
5513:
5508:
5503:
5499:
5498:
5497:
5488:
5480:
5414:
5412:
5411:
5406:
5404:
5394:
5393:
5377:
5355:
5354:
5338:
5313:
5312:
5296:
5274:
5273:
5257:
5238:
5235:
5226:
5225:
5209:
5150:
5148:
5147:
5142:
5140:
5138:
5124:
5113:
5108:
5107:
5064:
5062:
5061:
5056:
5029:
5026:
5024:
5022:
5005:
4994:
4989:
4988:
4950:
4948:
4947:
4942:
4940:
4926:
4900:
4871:
4845:
4826:
4823:
4810:
4771:= 1, to 1/2 for
4751:
4749:
4748:
4743:
4741:
4739:
4725:
4714:
4679:
4677:
4676:
4671:
4644:
4641:
4639:
4637:
4620:
4609:
4541:
4534:
4530:
4527:
4521:
4490:
4482:
4403:
4401:
4399:
4398:
4395:
4392:
4384:
4383:
4381:
4380:
4377:
4374:
4345:machine learning
4337:computer science
4242:
4236:
4230:
4221:with hypotenuse
4197:
4191:
4185:
4021:
4019:
4018:
4013:
4010:
4003:
4001:
4000:
3995:
3992:
3985:
3983:
3982:
3977:
3974:
3916:in series or to
3858:
3851:
3847:
3844:
3838:
3807:
3799:
3743:
3741:
3740:
3735:
3732:
3723:
3721:
3720:
3715:
3712:
3702:
3700:
3699:
3696:
3693:
3656:
3654:
3653:
3651:
3649:
3648:
3643:
3640:
3633:
3631:
3630:
3625:
3622:
3614:
3611:
3604:
3602:
3601:
3599:
3597:
3596:
3591:
3588:
3579:
3577:
3576:
3571:
3568:
3558:
3555:
3544:
3542:
3541:
3538:
3535:
3471:
3469:
3468:
3463:
3458:
3457:
3449:
3445:
3443:
3442:
3441:
3431:
3426:
3410:
3408:
3400:
3391:
3390:
3380:
3375:
3359:
3349:
3347:
3346:
3344:
3343:
3334:
3333:
3324:
3321:
3316:
3300:
3299:
3298:
3288:
3283:
3267:
3245:
3243:
3242:
3237:
3235:
3234:
3218:
3216:
3215:
3210:
3208:
3207:
3191:
3189:
3188:
3183:
3181:
3180:
3164:
3162:
3161:
3156:
3154:
3153:
3128:
3121:
3117:
3114:
3108:
3077:
3069:
3060:
3058:
3057:
3052:
3047:
3046:
3041:
3037:
3036:
3028:
3014:
3006:
2995:
2993:
2992:
2983:
2982:
2973:
2968:
2966:
2965:
2956:
2955:
2946:
2915:
2913:
2912:
2907:
2902:
2900:
2899:
2898:
2889:
2888:
2876:
2875:
2866:
2865:
2853:
2852:
2843:
2842:
2832:
2831:
2830:
2821:
2820:
2811:
2810:
2797:
2779:
2777:
2776:
2771:
2769:
2768:
2752:
2750:
2749:
2744:
2742:
2741:
2725:
2723:
2722:
2717:
2715:
2714:
2690:
2688:
2687:
2682:
2680:
2672:
2637:
2635:
2634:
2629:
2621:
2612:
2599:
2597:
2596:
2591:
2586:
2582:
2574:
2562:
2557:
2556:
2547:
2529:
2527:
2526:
2521:
2516:
2514:
2513:
2504:
2503:
2494:
2476:
2474:
2473:
2468:
2466:
2461:
2460:
2459:
2447:
2446:
2436:
2415:
2413:
2412:
2407:
2402:
2397:
2393:
2392:
2383:
2366:
2365:
2356:
2344:
2339:
2331:
2321:
2319:
2318:
2313:
2310:
2308:
2307:
2306:
2294:
2293:
2283:
2282:
2281:
2272:
2271:
2258:
2240:
2238:
2237:
2232:
2230:
2229:
2213:
2211:
2210:
2205:
2203:
2202:
2166:of two numbers,
2153:
2151:
2150:
2145:
2072:of two numbers,
2052:
2045:
2041:
2038:
2032:
2001:
1993:
1978:
1976:
1975:
1970:
1965:
1963:
1962:
1958:
1957:
1956:
1955:
1945:
1940:
1924:
1922:
1921:
1909:
1898:
1897:
1896:
1886:
1881:
1865:
1863:
1862:
1850:
1845:
1844:
1843:
1833:
1828:
1812:
1810:
1809:
1797:
1786:
1785:
1780:
1776:
1775:
1771:
1770:
1769:
1751:
1750:
1727:
1722:
1720:
1719:
1715:
1714:
1713:
1695:
1694:
1685:
1684:
1666:
1665:
1653:
1652:
1643:
1642:
1630:
1629:
1617:
1616:
1607:
1606:
1588:
1587:
1582:
1578:
1577:
1573:
1572:
1571:
1553:
1552:
1529:
1524:
1520:
1519:
1518:
1500:
1499:
1430:
1428:
1427:
1422:
1420:
1418:
1416:
1408:
1389:
1381:
1368:
1360:
1347:
1342:
1338:
1337:
1336:
1318:
1317:
1305:
1304:
1290:
1289:
1274:
1270:
1269:
1268:
1250:
1249:
1237:
1236:
1170:
1155:
1144:
1133:
1122:
1111:
1104:root mean square
1100:
1058:
1056:
1055:
1050:
1045:
1044:
1032:
1031:
1007:
1006:
994:
993:
972:
971:
959:
958:
930:
928:
927:
922:
917:
916:
906:
901:
886:
877:
868:
867:
849:
848:
836:
835:
810:
808:
807:
802:
800:
793:
790:
786:
785:
783:
782:
770:
762:
760:
759:
747:
742:
740:
739:
727:
713:
701:
700:
682:
681:
669:
668:
646:
643:
639:
638:
636:
635:
623:
615:
613:
612:
600:
595:
593:
592:
580:
566:
554:
553:
535:
534:
522:
521:
485:
483:
482:
477:
472:
469:
467:
466:
454:
451:
446:
427:
422:
419:
417:
416:
404:
393:
391:
390:
378:
373:
371:
370:
358:
352:
344:
343:
325:
324:
312:
311:
286:
284:
283:
278:
276:
275:
257:
256:
244:
243:
225:of the positive
212:
210:
209:
204:
192:
184:
179:
177:
176:
168:
163:
155:
150:
142:
136:
131:
130:
122:
118:
113:
112:
111:
96:
95:
80:
79:
66:
11515:
11514:
11510:
11509:
11508:
11506:
11505:
11504:
11490:
11489:
11488:
11483:
11446:
11417:
11379:
11316:
11302:quality control
11269:
11251:Clinical trials
11228:
11203:
11187:
11175:Hazard function
11169:
11123:
11085:
11069:
11032:
11028:BreuschāGodfrey
11016:
10993:
10933:
10908:Factor analysis
10854:
10835:Graphical model
10807:
10774:
10741:
10727:
10707:
10661:
10628:
10590:
10553:
10552:
10521:
10465:
10452:
10444:
10436:
10420:
10405:
10384:Rank statistics
10378:
10357:Model selection
10345:
10303:Goodness of fit
10297:
10274:
10248:
10220:
10173:
10118:
10107:Median unbiased
10035:
9946:
9879:Order statistic
9841:
9820:
9787:
9761:
9713:
9668:
9611:
9609:Data collection
9590:
9502:
9457:
9431:
9409:
9369:
9321:
9238:Continuous data
9228:
9215:
9197:
9192:
9141:"Harmonic Mean"
9132:
9127:
9126:
9121:
9117:
9112:
9108:
9092:
9091:
9085:
9083:
9079:
9072:
9070:"Archived copy"
9068:
9066:
9057:
9052:
9048:
9036:
9032:
9027:
9023:
9018:
9011:
9006:
9002:
8997:
8993:
8981:
8977:
8972:
8968:
8963:
8959:
8954:
8947:
8942:
8938:
8933:
8929:
8924:
8920:
8903:
8899:
8890:
8886:
8859:
8855:
8843:
8839:
8827:
8823:
8821:
8818:
8817:
8815:
8811:
8804:
8782:
8778:
8749:(3ā4): 98ā110.
8739:
8735:
8728:
8715:
8714:
8710:
8703:
8695:. p. 168.
8685:
8681:
8671:
8669:
8656:
8655:
8651:
8641:
8639:
8626:
8625:
8621:
8616:
8612:
8595:
8594:
8588:
8586:
8582:
8575:
8573:"Archived copy"
8571:
8562:
8558:
8547:
8543:
8527:
8523:
8518:Wayback Machine
8508:
8504:
8495:
8493:
8487:"Harmonic Mean"
8483:
8479:
8474:Wayback Machine
8465:
8461:
8456:
8451:
8450:
8436:
8433:
8430:
8429:
8427:
8420:
8417:
8414:
8413:
8411:
8404:
8401:
8398:
8397:
8395:
8389:
8381:
8379:
8371:
8365:
8339:
8335:
8330:
8287:Harmonic number
8267:
8260:
8257:
8247:In geophysical
8238:
8231:
8224:
8217:
8210:
8188:
8187:
8170:
8165:
8154:
8152:
8145:
8141:
8124:
8120:
8113:
8109:
8100:
8096:
8092:
8090:
8087:
8086:
8069:
8064:
8053:
8051:
8044:
8040:
8030:
8018:
8014:
8007:
8003:
7994:
7990:
7986:
7984:
7980:
7978:
7975:
7974:
7969:
7959:
7937:
7936:
7924:
7920:
7914:
7910:
7909:
7907:
7900:
7890:
7886:
7882:
7873:
7872:
7860:
7856:
7852:
7850:
7843:
7833:
7829:
7825:
7815:
7813:
7810:
7809:
7804:
7792:
7785:
7760:
7731:
7727:
7726:
7722:
7721:
7708:
7699:
7695:
7693:
7690:
7689:
7659:
7655:
7642:
7634:
7631:
7630:
7610:
7609:
7598:
7594:
7584:
7577:
7573:
7560:
7554:
7550:
7547:
7546:
7521:
7520:
7514:
7486:
7482:
7469:
7468:
7464:
7457:
7453:
7452:
7450:
7443:
7437:
7433:
7430:
7429:
7412:
7408:
7404:
7399:
7392:
7386:
7382:
7378:
7376:
7373:
7372:
7358:
7325:
7321:
7314:
7310:
7292:
7288:
7268:
7265:
7264:
7231:
7227:
7223:
7216:
7199:
7195:
7191:
7184:
7182:
7166:
7162:
7158:
7150:
7147:
7146:
7099:
7094:
7077:
7073:
7065:
7062:
7061:
7047:
7016:
7012:
7007:
7003:
6981:
6977:
6964:
6959:
6955:
6947:
6944:
6943:
6925:
6890:
6886:
6862:
6858:
6849:
6845:
6843:
6840:
6839:
6798:
6794:
6788:
6784:
6782:
6775:
6771:
6747:
6743:
6741:
6738:
6737:
6694:
6692:
6674:
6670:
6668:
6665:
6664:
6632:
6596:
6586:
6582:
6572:
6571:
6552:
6550:
6548:
6545:
6544:
6520:
6516:
6515:
6502:
6494:
6491:
6490:
6486:is then taken:
6485:
6446:
6434:
6429:
6418:
6416:
6407:
6403:
6401:
6398:
6397:
6391:
6353:
6349:
6344:
6336:
6333:
6332:
6315:
6278:
6274:
6259:
6255:
6253:
6250:
6249:
6216:
6203:
6195:
6192:
6191:
6158:
6154:
6148:
6144:
6142:
6132:
6112:
6109:
6108:
6090:
6079:
6073:
6070:
6055:
6039:
6028:
5984:
5980:
5976:
5949:
5948:
5944:
5937:
5933:
5929:
5927:
5910:
5906:
5898:
5895:
5894:
5865:
5861:
5860:
5833:
5832:
5828:
5821:
5817:
5813:
5811:
5802:
5798:
5796:
5793:
5792:
5778:
5758:
5716:
5709:
5705:
5694:
5691:
5690:
5680:
5655:
5651:
5642:
5638:
5633:
5630:
5629:
5621:The geometric (
5609:
5580:
5575:
5551:
5547:
5545:
5543:
5540:
5539:
5493:
5489:
5479:
5472:
5468:
5454:
5451:
5450:
5432:
5402:
5401:
5383:
5379:
5367:
5356:
5344:
5340:
5328:
5321:
5320:
5302:
5298:
5286:
5275:
5263:
5259:
5247:
5240:
5239:
5234:
5227:
5215:
5211:
5199:
5191:
5189:
5186:
5185:
5125:
5114:
5112:
5097:
5093:
5091:
5088:
5087:
5025:
5006:
4995:
4993:
4978:
4974:
4972:
4969:
4968:
4963:
4938:
4937:
4916:
4905:
4890:
4883:
4882:
4861:
4850:
4835:
4828:
4827:
4822:
4815:
4800:
4792:
4790:
4787:
4786:
4726:
4715:
4713:
4705:
4702:
4701:
4640:
4621:
4610:
4608:
4600:
4597:
4596:
4542:
4531:
4525:
4522:
4507:
4491:
4480:
4471:nuclear physics
4396:
4393:
4390:
4389:
4387:
4386:
4378:
4375:
4372:
4371:
4369:
4368:
4339:, specifically
4333:
4238:
4232:
4226:
4193:
4187:
4181:
4101:
4089:
4082:
4075:
4068:
4057:
4050:
4043:
4034:from the lens.
4014:
4011:
4008:
4007:
4005:
3996:
3993:
3990:
3989:
3987:
3978:
3975:
3972:
3971:
3969:
3963:optic equations
3959:
3896:(e.g., 60
3886:
3880:
3859:
3848:
3842:
3839:
3824:
3808:
3797:
3790:
3785:arithmetic mean
3782:
3778:
3736:
3733:
3728:
3727:
3725:
3716:
3713:
3708:
3707:
3705:
3703:
3697:
3694:
3691:
3690:
3688:
3673:arithmetic mean
3652:
3644:
3641:
3638:
3637:
3635:
3626:
3623:
3620:
3619:
3617:
3615:
3612:
3609:
3608:
3606:
3600:
3592:
3589:
3584:
3583:
3581:
3572:
3569:
3564:
3563:
3561:
3559:
3556:
3550:
3549:
3547:
3545:
3539:
3536:
3533:
3532:
3530:
3491:
3486:
3481:
3450:
3437:
3433:
3427:
3416:
3411:
3401:
3396:
3386:
3382:
3376:
3365:
3360:
3358:
3354:
3353:
3339:
3335:
3329:
3325:
3323:
3317:
3306:
3301:
3294:
3290:
3284:
3273:
3268:
3266:
3258:
3255:
3254:
3250:is defined by
3230:
3226:
3224:
3221:
3220:
3203:
3199:
3197:
3194:
3193:
3176:
3172:
3170:
3167:
3166:
3149:
3145:
3143:
3140:
3139:
3129:
3118:
3112:
3109:
3094:
3078:
3067:
3042:
3027:
3020:
3016:
3015:
3005:
2988:
2984:
2978:
2974:
2972:
2961:
2957:
2951:
2947:
2945:
2943:
2940:
2939:
2894:
2890:
2884:
2880:
2871:
2867:
2861:
2857:
2848:
2844:
2838:
2834:
2833:
2826:
2822:
2816:
2812:
2806:
2802:
2798:
2796:
2788:
2785:
2784:
2764:
2760:
2758:
2755:
2754:
2737:
2733:
2731:
2728:
2727:
2710:
2706:
2704:
2701:
2700:
2697:
2671:
2663:
2660:
2659:
2610:
2608:
2605:
2604:
2573:
2569:
2552:
2548:
2546:
2538:
2535:
2534:
2509:
2505:
2499:
2495:
2493:
2485:
2482:
2481:
2455:
2451:
2442:
2438:
2437:
2435:
2427:
2424:
2423:
2421:arithmetic mean
2388:
2384:
2379:
2361:
2357:
2352:
2345:
2343:
2330:
2327:
2324:
2323:
2302:
2298:
2289:
2285:
2284:
2277:
2273:
2267:
2263:
2259:
2257:
2249:
2246:
2245:
2225:
2221:
2219:
2216:
2215:
2198:
2194:
2192:
2189:
2188:
2121:
2118:
2117:
2092:in red and the
2086:arithmetic mean
2062:
2053:
2042:
2036:
2033:
2018:
2002:
1991:
1951:
1947:
1941:
1930:
1925:
1917:
1913:
1908:
1892:
1888:
1882:
1871:
1866:
1858:
1854:
1849:
1839:
1835:
1829:
1818:
1813:
1805:
1801:
1796:
1795:
1791:
1787:
1781:
1765:
1761:
1746:
1742:
1741:
1737:
1733:
1729:
1728:
1726:
1703:
1699:
1690:
1686:
1680:
1676:
1661:
1657:
1648:
1644:
1638:
1634:
1625:
1621:
1612:
1608:
1602:
1598:
1597:
1593:
1589:
1583:
1567:
1563:
1548:
1544:
1543:
1539:
1535:
1531:
1530:
1528:
1514:
1510:
1495:
1491:
1490:
1486:
1481:
1478:
1477:
1409:
1404:
1382:
1377:
1361:
1356:
1351:
1346:
1332:
1328:
1313:
1309:
1300:
1296:
1295:
1291:
1282:
1278:
1264:
1260:
1245:
1241:
1232:
1228:
1227:
1223:
1218:
1215:
1214:
1208:
1192:arithmetic mean
1157:
1146:
1135:
1126:arithmetic mean
1124:
1113:
1102:
1087:
1076:
1040:
1036:
1027:
1023:
1002:
998:
989:
985:
967:
963:
954:
950:
942:
939:
938:
912:
908:
902:
891:
875:
863:
859:
844:
840:
831:
827:
819:
816:
815:
798:
797:
778:
774:
769:
755:
751:
746:
735:
731:
726:
725:
721:
712:
705:
696:
692:
677:
673:
664:
660:
651:
650:
631:
627:
622:
608:
604:
599:
588:
584:
579:
578:
574:
565:
558:
549:
545:
530:
526:
517:
513:
503:
501:
498:
497:
491:arithmetic mean
462:
458:
453:
447:
436:
426:
412:
408:
403:
386:
382:
377:
366:
362:
357:
351:
339:
335:
320:
316:
307:
303:
295:
292:
291:
271:
267:
252:
248:
239:
235:
233:
230:
229:
219:
183:
167:
154:
141:
140:
135:
123:
104:
100:
88:
84:
72:
68:
67:
65:
61:
60:
58:
55:
54:
48:arithmetic mean
17:
12:
11:
5:
11513:
11503:
11502:
11485:
11484:
11482:
11481:
11469:
11457:
11443:
11430:
11427:
11426:
11423:
11422:
11419:
11418:
11416:
11415:
11410:
11405:
11400:
11395:
11389:
11387:
11381:
11380:
11378:
11377:
11372:
11367:
11362:
11357:
11352:
11347:
11342:
11337:
11332:
11326:
11324:
11318:
11317:
11315:
11314:
11309:
11304:
11295:
11290:
11285:
11279:
11277:
11271:
11270:
11268:
11267:
11262:
11257:
11248:
11246:Bioinformatics
11242:
11240:
11230:
11229:
11217:
11216:
11213:
11212:
11209:
11208:
11205:
11204:
11202:
11201:
11195:
11193:
11189:
11188:
11186:
11185:
11179:
11177:
11171:
11170:
11168:
11167:
11162:
11157:
11152:
11146:
11144:
11135:
11129:
11128:
11125:
11124:
11122:
11121:
11116:
11111:
11106:
11101:
11095:
11093:
11087:
11086:
11084:
11083:
11078:
11073:
11065:
11060:
11055:
11054:
11053:
11051:partial (PACF)
11042:
11040:
11034:
11033:
11031:
11030:
11025:
11020:
11012:
11007:
11001:
10999:
10998:Specific tests
10995:
10994:
10992:
10991:
10986:
10981:
10976:
10971:
10966:
10961:
10956:
10950:
10948:
10941:
10935:
10934:
10932:
10931:
10930:
10929:
10928:
10927:
10912:
10911:
10910:
10900:
10898:Classification
10895:
10890:
10885:
10880:
10875:
10870:
10864:
10862:
10856:
10855:
10853:
10852:
10847:
10845:McNemar's test
10842:
10837:
10832:
10827:
10821:
10819:
10809:
10808:
10784:
10783:
10780:
10779:
10776:
10775:
10773:
10772:
10767:
10762:
10757:
10751:
10749:
10743:
10742:
10740:
10739:
10723:
10717:
10715:
10709:
10708:
10706:
10705:
10700:
10695:
10690:
10685:
10683:Semiparametric
10680:
10675:
10669:
10667:
10663:
10662:
10660:
10659:
10654:
10649:
10644:
10638:
10636:
10630:
10629:
10627:
10626:
10621:
10616:
10611:
10606:
10600:
10598:
10592:
10591:
10589:
10588:
10583:
10578:
10573:
10567:
10565:
10555:
10554:
10551:
10550:
10545:
10539:
10531:
10530:
10527:
10526:
10523:
10522:
10520:
10519:
10518:
10517:
10507:
10502:
10497:
10496:
10495:
10490:
10479:
10477:
10471:
10470:
10467:
10466:
10464:
10463:
10458:
10457:
10456:
10448:
10440:
10424:
10421:(MannāWhitney)
10416:
10415:
10414:
10401:
10400:
10399:
10388:
10386:
10380:
10379:
10377:
10376:
10375:
10374:
10369:
10364:
10354:
10349:
10346:(ShapiroāWilk)
10341:
10336:
10331:
10326:
10321:
10313:
10307:
10305:
10299:
10298:
10296:
10295:
10287:
10278:
10266:
10260:
10258:Specific tests
10254:
10253:
10250:
10249:
10247:
10246:
10241:
10236:
10230:
10228:
10222:
10221:
10219:
10218:
10213:
10212:
10211:
10201:
10200:
10199:
10189:
10183:
10181:
10175:
10174:
10172:
10171:
10170:
10169:
10164:
10154:
10149:
10144:
10139:
10134:
10128:
10126:
10120:
10119:
10117:
10116:
10111:
10110:
10109:
10104:
10103:
10102:
10097:
10082:
10081:
10080:
10075:
10070:
10065:
10054:
10052:
10043:
10037:
10036:
10034:
10033:
10028:
10023:
10022:
10021:
10011:
10006:
10005:
10004:
9994:
9993:
9992:
9987:
9982:
9972:
9967:
9962:
9961:
9960:
9955:
9950:
9934:
9933:
9932:
9927:
9922:
9912:
9911:
9910:
9905:
9895:
9894:
9893:
9883:
9882:
9881:
9871:
9866:
9861:
9855:
9853:
9843:
9842:
9830:
9829:
9826:
9825:
9822:
9821:
9819:
9818:
9813:
9808:
9803:
9797:
9795:
9789:
9788:
9786:
9785:
9780:
9775:
9769:
9767:
9763:
9762:
9760:
9759:
9754:
9749:
9744:
9739:
9734:
9729:
9723:
9721:
9715:
9714:
9712:
9711:
9709:Standard error
9706:
9701:
9696:
9695:
9694:
9689:
9678:
9676:
9670:
9669:
9667:
9666:
9661:
9656:
9651:
9646:
9641:
9639:Optimal design
9636:
9631:
9625:
9623:
9613:
9612:
9600:
9599:
9596:
9595:
9592:
9591:
9589:
9588:
9583:
9578:
9573:
9568:
9563:
9558:
9553:
9548:
9543:
9538:
9533:
9528:
9523:
9518:
9512:
9510:
9504:
9503:
9501:
9500:
9495:
9494:
9493:
9488:
9478:
9473:
9467:
9465:
9459:
9458:
9456:
9455:
9450:
9445:
9439:
9437:
9436:Summary tables
9433:
9432:
9430:
9429:
9423:
9421:
9415:
9414:
9411:
9410:
9408:
9407:
9406:
9405:
9400:
9395:
9385:
9379:
9377:
9371:
9370:
9368:
9367:
9362:
9357:
9352:
9347:
9342:
9337:
9331:
9329:
9323:
9322:
9320:
9319:
9314:
9309:
9308:
9307:
9302:
9297:
9292:
9287:
9282:
9277:
9272:
9270:Contraharmonic
9267:
9262:
9251:
9249:
9240:
9230:
9229:
9217:
9216:
9214:
9213:
9208:
9202:
9199:
9198:
9191:
9190:
9183:
9176:
9168:
9162:
9161:
9152:
9131:
9130:External links
9128:
9125:
9124:
9115:
9106:
9055:
9046:
9030:
9021:
9009:
9000:
8991:
8975:
8966:
8957:
8945:
8936:
8927:
8918:
8897:
8884:
8865:
8862:
8858:
8854:
8849:
8846:
8842:
8838:
8833:
8830:
8826:
8809:
8802:
8776:
8733:
8726:
8708:
8702:978-0805385663
8701:
8693:Addison Wesley
8679:
8649:
8619:
8610:
8556:
8541:
8521:
8502:
8477:
8458:
8457:
8455:
8452:
8449:
8448:
8332:
8331:
8329:
8326:
8325:
8324:
8319:
8314:
8309:
8307:Geometric mean
8304:
8299:
8294:
8289:
8284:
8279:
8273:
8272:
8256:
8253:
8237:
8234:
8229:
8222:
8215:
8208:
8202:
8201:
8185:
8179:
8173:
8168:
8164:
8160:
8157:
8151:
8148:
8144:
8138:
8133:
8127:
8123:
8119:
8116:
8112:
8108:
8103:
8099:
8095:
8089:
8088:
8084:
8078:
8072:
8067:
8063:
8059:
8056:
8050:
8047:
8043:
8036:
8033:
8027:
8021:
8017:
8013:
8010:
8006:
8002:
7997:
7993:
7989:
7983:
7982:
7967:
7957:
7951:
7950:
7933:
7927:
7923:
7917:
7913:
7906:
7903:
7901:
7898:
7893:
7889:
7885:
7881:
7878:
7875:
7874:
7869:
7863:
7859:
7855:
7849:
7846:
7844:
7841:
7836:
7832:
7828:
7824:
7821:
7818:
7817:
7802:
7791:
7788:
7783:
7777:
7776:
7763:
7758:
7754:
7751:
7748:
7745:
7742:
7739:
7734:
7730:
7725:
7720:
7715:
7712:
7707:
7702:
7698:
7687:
7676:
7673:
7670:
7667:
7662:
7658:
7654:
7649:
7646:
7641:
7638:
7624:
7623:
7607:
7601:
7597:
7591:
7588:
7583:
7580:
7576:
7572:
7569:
7566:
7563:
7561:
7557:
7553:
7549:
7548:
7542:
7539:
7536:
7533:
7528:
7525:
7517:
7512:
7507:
7503:
7500:
7497:
7494:
7489:
7485:
7481:
7476:
7473:
7467:
7463:
7460:
7456:
7449:
7446:
7444:
7440:
7436:
7432:
7431:
7424:
7419:
7416:
7411:
7407:
7403:
7398:
7395:
7393:
7389:
7385:
7381:
7380:
7357:
7354:
7350:
7349:
7337:
7331:
7328:
7324:
7320:
7317:
7313:
7309:
7306:
7303:
7298:
7295:
7291:
7287:
7284:
7281:
7278:
7275:
7272:
7258:
7257:
7246:
7239:
7234:
7230:
7226:
7222:
7219:
7213:
7208:
7205:
7202:
7198:
7194:
7190:
7187:
7181:
7177:
7172:
7169:
7165:
7161:
7157:
7154:
7129:
7128:
7114:
7111:
7108:
7105:
7102:
7098:
7093:
7089:
7084:
7081:
7076:
7072:
7069:
7049:Assuming that
7046:
7043:
7042:
7041:
7030:
7026:
7019:
7015:
7011:
7006:
7002:
6999:
6996:
6992:
6984:
6980:
6976:
6973:
6970:
6967:
6963:
6958:
6954:
6951:
6924:
6921:
6910:
6909:
6896:
6893:
6889:
6885:
6882:
6879:
6876:
6873:
6868:
6865:
6861:
6857:
6852:
6848:
6822:
6821:
6809:
6801:
6797:
6791:
6787:
6781:
6778:
6774:
6770:
6767:
6764:
6761:
6758:
6755:
6750:
6746:
6727:
6726:
6713:
6709:
6706:
6703:
6700:
6697:
6691:
6688:
6685:
6682:
6677:
6673:
6631:
6628:
6616:
6615:
6604:
6599:
6594:
6589:
6585:
6581:
6578:
6575:
6570:
6565:
6561:
6558:
6555:
6538:
6537:
6523:
6519:
6514:
6509:
6506:
6501:
6498:
6483:
6473:
6472:
6461:
6453:
6450:
6443:
6440:
6437:
6433:
6427:
6424:
6421:
6415:
6410:
6406:
6389:
6377:
6376:
6360:
6357:
6352:
6348:
6343:
6340:
6314:
6311:
6303:
6302:
6290:
6285:
6282:
6277:
6273:
6270:
6267:
6262:
6258:
6240:
6239:
6228:
6223:
6220:
6215:
6210:
6207:
6202:
6199:
6177:
6176:
6161:
6157:
6151:
6147:
6139:
6136:
6131:
6128:
6125:
6122:
6119:
6116:
6092:
6091:
6042:
6040:
6033:
6027:
6024:
6004:
6003:
5987:
5983:
5979:
5973:
5968:
5964:
5961:
5956:
5953:
5947:
5943:
5940:
5936:
5932:
5926:
5922:
5917:
5914:
5909:
5905:
5902:
5888:
5887:
5873:
5868:
5864:
5857:
5852:
5848:
5845:
5840:
5837:
5831:
5827:
5824:
5820:
5816:
5810:
5805:
5801:
5777:
5774:
5757:
5754:
5742:
5741:
5729:
5723:
5720:
5715:
5712:
5708:
5704:
5701:
5698:
5679:
5676:
5675:
5674:
5663:
5658:
5654:
5650:
5645:
5641:
5637:
5607:
5601:
5600:
5589:
5583:
5578:
5574:
5570:
5567:
5564:
5559:
5554:
5550:
5518:
5517:
5506:
5502:
5496:
5492:
5486:
5483:
5478:
5475:
5471:
5467:
5464:
5461:
5458:
5431:
5428:
5416:
5415:
5400:
5397:
5392:
5389:
5386:
5382:
5376:
5373:
5370:
5366:
5362:
5359:
5357:
5353:
5350:
5347:
5343:
5337:
5334:
5331:
5327:
5323:
5322:
5319:
5316:
5311:
5308:
5305:
5301:
5295:
5292:
5289:
5285:
5281:
5278:
5276:
5272:
5269:
5266:
5262:
5256:
5253:
5250:
5246:
5242:
5241:
5233:
5230:
5228:
5224:
5221:
5218:
5214:
5208:
5205:
5202:
5198:
5194:
5193:
5152:
5151:
5137:
5134:
5131:
5128:
5123:
5120:
5117:
5111:
5106:
5103:
5100:
5096:
5066:
5065:
5054:
5051:
5048:
5043:
5038:
5035:
5032:
5021:
5018:
5015:
5012:
5009:
5004:
5001:
4998:
4992:
4987:
4984:
4981:
4977:
4961:
4952:
4951:
4936:
4933:
4930:
4925:
4922:
4919:
4915:
4911:
4908:
4906:
4904:
4899:
4896:
4893:
4889:
4885:
4884:
4881:
4878:
4875:
4870:
4867:
4864:
4860:
4856:
4853:
4851:
4849:
4844:
4841:
4838:
4834:
4830:
4829:
4821:
4818:
4816:
4814:
4809:
4806:
4803:
4799:
4795:
4794:
4753:
4752:
4738:
4735:
4732:
4729:
4724:
4721:
4718:
4712:
4709:
4681:
4680:
4669:
4666:
4663:
4658:
4653:
4650:
4647:
4636:
4633:
4630:
4627:
4624:
4619:
4616:
4613:
4607:
4604:
4544:
4543:
4494:
4492:
4485:
4479:
4476:
4460:CAFE standards
4332:
4329:
4159:right triangle
4100:
4097:
4088:
4085:
4080:
4073:
4066:
4055:
4048:
4041:
3958:
3955:
3879:
3876:
3861:
3860:
3811:
3809:
3802:
3796:
3793:
3788:
3780:
3776:
3687:
3616:
3560:
3529:
3490:
3487:
3485:
3482:
3480:
3477:
3473:
3472:
3461:
3456:
3453:
3448:
3440:
3436:
3430:
3425:
3422:
3419:
3415:
3407:
3404:
3399:
3395:
3389:
3385:
3379:
3374:
3371:
3368:
3364:
3357:
3352:
3342:
3338:
3332:
3328:
3320:
3315:
3312:
3309:
3305:
3297:
3293:
3287:
3282:
3279:
3276:
3272:
3265:
3262:
3233:
3229:
3206:
3202:
3179:
3175:
3152:
3148:
3131:
3130:
3081:
3079:
3072:
3066:
3063:
3062:
3061:
3050:
3045:
3040:
3034:
3031:
3026:
3023:
3019:
3012:
3009:
3004:
3001:
2998:
2991:
2987:
2981:
2977:
2971:
2964:
2960:
2954:
2950:
2933:if and only if
2917:
2916:
2905:
2897:
2893:
2887:
2883:
2879:
2874:
2870:
2864:
2860:
2856:
2851:
2847:
2841:
2837:
2829:
2825:
2819:
2815:
2809:
2805:
2801:
2795:
2792:
2767:
2763:
2740:
2736:
2713:
2709:
2696:
2693:
2678:
2675:
2670:
2667:
2646:= 2 case that
2627:
2624:
2618:
2615:
2601:
2600:
2589:
2585:
2580:
2577:
2572:
2568:
2565:
2560:
2555:
2551:
2545:
2542:
2519:
2512:
2508:
2502:
2498:
2492:
2489:
2479:geometric mean
2464:
2458:
2454:
2450:
2445:
2441:
2434:
2431:
2417:
2416:
2405:
2400:
2396:
2391:
2387:
2382:
2378:
2375:
2372:
2369:
2364:
2360:
2355:
2351:
2348:
2342:
2337:
2334:
2305:
2301:
2297:
2292:
2288:
2280:
2276:
2270:
2266:
2262:
2256:
2253:
2228:
2224:
2201:
2197:
2143:
2140:
2137:
2134:
2131:
2128:
2125:
2114:right triangle
2106:quadratic mean
2094:geometric mean
2061:
2058:
2055:
2054:
2005:
2003:
1996:
1990:
1987:
1968:
1961:
1954:
1950:
1944:
1939:
1936:
1933:
1929:
1920:
1916:
1912:
1907:
1904:
1901:
1895:
1891:
1885:
1880:
1877:
1874:
1870:
1861:
1857:
1853:
1848:
1842:
1838:
1832:
1827:
1824:
1821:
1817:
1808:
1804:
1800:
1794:
1790:
1784:
1779:
1774:
1768:
1764:
1760:
1757:
1754:
1749:
1745:
1740:
1736:
1732:
1725:
1718:
1712:
1709:
1706:
1702:
1698:
1693:
1689:
1683:
1679:
1675:
1672:
1669:
1664:
1660:
1656:
1651:
1647:
1641:
1637:
1633:
1628:
1624:
1620:
1615:
1611:
1605:
1601:
1596:
1592:
1586:
1581:
1576:
1570:
1566:
1562:
1559:
1556:
1551:
1547:
1542:
1538:
1534:
1527:
1523:
1517:
1513:
1509:
1506:
1503:
1498:
1494:
1489:
1485:
1415:
1412:
1407:
1403:
1399:
1396:
1393:
1388:
1385:
1380:
1376:
1372:
1367:
1364:
1359:
1355:
1350:
1345:
1341:
1335:
1331:
1327:
1324:
1321:
1316:
1312:
1308:
1303:
1299:
1294:
1288:
1285:
1281:
1277:
1273:
1267:
1263:
1259:
1256:
1253:
1248:
1244:
1240:
1235:
1231:
1226:
1222:
1206:
1196:geometric mean
1137:geometric mean
1115:quadratic mean
1075:
1072:
1048:
1043:
1039:
1035:
1030:
1026:
1022:
1019:
1016:
1013:
1010:
1005:
1001:
997:
992:
988:
984:
981:
978:
975:
970:
966:
962:
957:
953:
949:
946:
920:
915:
911:
905:
900:
897:
894:
890:
883:
880:
874:
871:
866:
862:
858:
855:
852:
847:
843:
839:
834:
830:
826:
823:
812:
811:
796:
789:
781:
777:
773:
768:
765:
758:
754:
750:
745:
738:
734:
730:
724:
720:
716:
711:
708:
706:
704:
699:
695:
691:
688:
685:
680:
676:
672:
667:
663:
659:
656:
653:
652:
649:
642:
634:
630:
626:
621:
618:
611:
607:
603:
598:
591:
587:
583:
577:
573:
569:
564:
561:
559:
557:
552:
548:
544:
541:
538:
533:
529:
525:
520:
516:
512:
509:
506:
505:
487:
486:
475:
465:
461:
457:
450:
445:
442:
439:
435:
430:
425:
415:
411:
407:
402:
399:
396:
389:
385:
381:
376:
369:
365:
361:
355:
350:
347:
342:
338:
334:
331:
328:
323:
319:
315:
310:
306:
302:
299:
274:
270:
266:
263:
260:
255:
251:
247:
242:
238:
218:
215:
214:
213:
202:
198:
195:
190:
187:
182:
174:
171:
166:
161:
158:
153:
148:
145:
139:
134:
129:
126:
121:
116:
110:
107:
103:
99:
94:
91:
87:
83:
78:
75:
71:
64:
15:
9:
6:
4:
3:
2:
11512:
11501:
11498:
11497:
11495:
11480:
11479:
11470:
11468:
11467:
11458:
11456:
11455:
11450:
11444:
11442:
11441:
11432:
11431:
11428:
11414:
11411:
11409:
11408:Geostatistics
11406:
11404:
11401:
11399:
11396:
11394:
11391:
11390:
11388:
11386:
11382:
11376:
11375:Psychometrics
11373:
11371:
11368:
11366:
11363:
11361:
11358:
11356:
11353:
11351:
11348:
11346:
11343:
11341:
11338:
11336:
11333:
11331:
11328:
11327:
11325:
11323:
11319:
11313:
11310:
11308:
11305:
11303:
11299:
11296:
11294:
11291:
11289:
11286:
11284:
11281:
11280:
11278:
11276:
11272:
11266:
11263:
11261:
11258:
11256:
11252:
11249:
11247:
11244:
11243:
11241:
11239:
11238:Biostatistics
11235:
11231:
11227:
11222:
11218:
11200:
11199:Log-rank test
11197:
11196:
11194:
11190:
11184:
11181:
11180:
11178:
11176:
11172:
11166:
11163:
11161:
11158:
11156:
11153:
11151:
11148:
11147:
11145:
11143:
11139:
11136:
11134:
11130:
11120:
11117:
11115:
11112:
11110:
11107:
11105:
11102:
11100:
11097:
11096:
11094:
11092:
11088:
11082:
11079:
11077:
11074:
11072:
11070:(BoxāJenkins)
11066:
11064:
11061:
11059:
11056:
11052:
11049:
11048:
11047:
11044:
11043:
11041:
11039:
11035:
11029:
11026:
11024:
11023:DurbināWatson
11021:
11019:
11013:
11011:
11008:
11006:
11005:DickeyāFuller
11003:
11002:
11000:
10996:
10990:
10987:
10985:
10982:
10980:
10979:Cointegration
10977:
10975:
10972:
10970:
10967:
10965:
10962:
10960:
10957:
10955:
10954:Decomposition
10952:
10951:
10949:
10945:
10942:
10940:
10936:
10926:
10923:
10922:
10921:
10918:
10917:
10916:
10913:
10909:
10906:
10905:
10904:
10901:
10899:
10896:
10894:
10891:
10889:
10886:
10884:
10881:
10879:
10876:
10874:
10871:
10869:
10866:
10865:
10863:
10861:
10857:
10851:
10848:
10846:
10843:
10841:
10838:
10836:
10833:
10831:
10828:
10826:
10825:Cohen's kappa
10823:
10822:
10820:
10818:
10814:
10810:
10806:
10802:
10798:
10794:
10789:
10785:
10771:
10768:
10766:
10763:
10761:
10758:
10756:
10753:
10752:
10750:
10748:
10744:
10738:
10734:
10730:
10724:
10722:
10719:
10718:
10716:
10714:
10710:
10704:
10701:
10699:
10696:
10694:
10691:
10689:
10686:
10684:
10681:
10679:
10678:Nonparametric
10676:
10674:
10671:
10670:
10668:
10664:
10658:
10655:
10653:
10650:
10648:
10645:
10643:
10640:
10639:
10637:
10635:
10631:
10625:
10622:
10620:
10617:
10615:
10612:
10610:
10607:
10605:
10602:
10601:
10599:
10597:
10593:
10587:
10584:
10582:
10579:
10577:
10574:
10572:
10569:
10568:
10566:
10564:
10560:
10556:
10549:
10546:
10544:
10541:
10540:
10536:
10532:
10516:
10513:
10512:
10511:
10508:
10506:
10503:
10501:
10498:
10494:
10491:
10489:
10486:
10485:
10484:
10481:
10480:
10478:
10476:
10472:
10462:
10459:
10455:
10449:
10447:
10441:
10439:
10433:
10432:
10431:
10428:
10427:Nonparametric
10425:
10423:
10417:
10413:
10410:
10409:
10408:
10402:
10398:
10397:Sample median
10395:
10394:
10393:
10390:
10389:
10387:
10385:
10381:
10373:
10370:
10368:
10365:
10363:
10360:
10359:
10358:
10355:
10353:
10350:
10348:
10342:
10340:
10337:
10335:
10332:
10330:
10327:
10325:
10322:
10320:
10318:
10314:
10312:
10309:
10308:
10306:
10304:
10300:
10294:
10292:
10288:
10286:
10284:
10279:
10277:
10272:
10268:
10267:
10264:
10261:
10259:
10255:
10245:
10242:
10240:
10237:
10235:
10232:
10231:
10229:
10227:
10223:
10217:
10214:
10210:
10207:
10206:
10205:
10202:
10198:
10195:
10194:
10193:
10190:
10188:
10185:
10184:
10182:
10180:
10176:
10168:
10165:
10163:
10160:
10159:
10158:
10155:
10153:
10150:
10148:
10145:
10143:
10140:
10138:
10135:
10133:
10130:
10129:
10127:
10125:
10121:
10115:
10112:
10108:
10105:
10101:
10098:
10096:
10093:
10092:
10091:
10088:
10087:
10086:
10083:
10079:
10076:
10074:
10071:
10069:
10066:
10064:
10061:
10060:
10059:
10056:
10055:
10053:
10051:
10047:
10044:
10042:
10038:
10032:
10029:
10027:
10024:
10020:
10017:
10016:
10015:
10012:
10010:
10007:
10003:
10002:loss function
10000:
9999:
9998:
9995:
9991:
9988:
9986:
9983:
9981:
9978:
9977:
9976:
9973:
9971:
9968:
9966:
9963:
9959:
9956:
9954:
9951:
9949:
9943:
9940:
9939:
9938:
9935:
9931:
9928:
9926:
9923:
9921:
9918:
9917:
9916:
9913:
9909:
9906:
9904:
9901:
9900:
9899:
9896:
9892:
9889:
9888:
9887:
9884:
9880:
9877:
9876:
9875:
9872:
9870:
9867:
9865:
9862:
9860:
9857:
9856:
9854:
9852:
9848:
9844:
9840:
9835:
9831:
9817:
9814:
9812:
9809:
9807:
9804:
9802:
9799:
9798:
9796:
9794:
9790:
9784:
9781:
9779:
9776:
9774:
9771:
9770:
9768:
9764:
9758:
9755:
9753:
9750:
9748:
9745:
9743:
9740:
9738:
9735:
9733:
9730:
9728:
9725:
9724:
9722:
9720:
9716:
9710:
9707:
9705:
9704:Questionnaire
9702:
9700:
9697:
9693:
9690:
9688:
9685:
9684:
9683:
9680:
9679:
9677:
9675:
9671:
9665:
9662:
9660:
9657:
9655:
9652:
9650:
9647:
9645:
9642:
9640:
9637:
9635:
9632:
9630:
9627:
9626:
9624:
9622:
9618:
9614:
9610:
9605:
9601:
9587:
9584:
9582:
9579:
9577:
9574:
9572:
9569:
9567:
9564:
9562:
9559:
9557:
9554:
9552:
9549:
9547:
9544:
9542:
9539:
9537:
9534:
9532:
9531:Control chart
9529:
9527:
9524:
9522:
9519:
9517:
9514:
9513:
9511:
9509:
9505:
9499:
9496:
9492:
9489:
9487:
9484:
9483:
9482:
9479:
9477:
9474:
9472:
9469:
9468:
9466:
9464:
9460:
9454:
9451:
9449:
9446:
9444:
9441:
9440:
9438:
9434:
9428:
9425:
9424:
9422:
9420:
9416:
9404:
9401:
9399:
9396:
9394:
9391:
9390:
9389:
9386:
9384:
9381:
9380:
9378:
9376:
9372:
9366:
9363:
9361:
9358:
9356:
9353:
9351:
9348:
9346:
9343:
9341:
9338:
9336:
9333:
9332:
9330:
9328:
9324:
9318:
9315:
9313:
9310:
9306:
9303:
9301:
9298:
9296:
9293:
9291:
9288:
9286:
9283:
9281:
9278:
9276:
9273:
9271:
9268:
9266:
9263:
9261:
9258:
9257:
9256:
9253:
9252:
9250:
9248:
9244:
9241:
9239:
9235:
9231:
9227:
9222:
9218:
9212:
9209:
9207:
9204:
9203:
9200:
9196:
9189:
9184:
9182:
9177:
9175:
9170:
9169:
9166:
9160:
9156:
9153:
9148:
9147:
9142:
9139:
9134:
9133:
9119:
9110:
9102:
9096:
9082:on 2010-06-11
9078:
9071:
9064:
9062:
9060:
9050:
9044:
9040:
9034:
9025:
9016:
9014:
9004:
8995:
8989:
8985:
8979:
8970:
8961:
8952:
8950:
8940:
8931:
8922:
8914:
8910:
8909:
8901:
8894:
8888:
8881:
8863:
8860:
8856:
8852:
8847:
8844:
8840:
8836:
8831:
8828:
8824:
8813:
8805:
8803:0-486-69154-3
8799:
8795:
8790:
8789:
8780:
8772:
8768:
8764:
8760:
8756:
8752:
8748:
8744:
8737:
8729:
8727:0-07-142967-0
8723:
8719:
8712:
8704:
8698:
8694:
8690:
8683:
8667:
8663:
8659:
8653:
8637:
8633:
8629:
8623:
8614:
8605:
8599:
8581:
8574:
8569:
8567:
8560:
8553:
8552:
8545:
8539:
8535:
8531:
8525:
8519:
8515:
8512:
8506:
8492:
8488:
8481:
8475:
8471:
8468:
8463:
8459:
8445:
8426:∴ HC =
8393:
8387:
8377:
8369:
8363:
8360:, and radius
8359:
8355:
8351:
8347:
8343:
8337:
8333:
8323:
8320:
8318:
8315:
8313:
8310:
8308:
8305:
8303:
8300:
8298:
8297:Weighted mean
8295:
8293:
8290:
8288:
8285:
8283:
8280:
8278:
8275:
8274:
8270:
8264:
8259:
8252:
8250:
8245:
8243:
8233:
8228:
8221:
8214:
8207:
8183:
8177:
8171:
8166:
8162:
8158:
8155:
8149:
8146:
8142:
8136:
8131:
8125:
8121:
8117:
8114:
8110:
8106:
8101:
8097:
8093:
8082:
8076:
8070:
8065:
8061:
8057:
8054:
8048:
8045:
8041:
8034:
8031:
8025:
8019:
8015:
8011:
8008:
8004:
8000:
7995:
7991:
7987:
7973:
7972:
7971:
7966:
7961:
7956:
7931:
7925:
7921:
7915:
7911:
7904:
7902:
7896:
7891:
7887:
7883:
7879:
7876:
7867:
7861:
7857:
7853:
7847:
7845:
7839:
7834:
7830:
7826:
7822:
7819:
7808:
7807:
7806:
7801:
7797:
7787:
7782:
7761:
7756:
7752:
7749:
7743:
7737:
7732:
7728:
7723:
7718:
7713:
7710:
7705:
7700:
7696:
7688:
7671:
7665:
7660:
7656:
7652:
7647:
7644:
7639:
7636:
7629:
7628:
7627:
7605:
7599:
7595:
7589:
7586:
7581:
7578:
7574:
7570:
7567:
7564:
7562:
7555:
7551:
7537:
7531:
7526:
7523:
7515:
7510:
7505:
7498:
7492:
7487:
7483:
7479:
7474:
7471:
7465:
7461:
7458:
7454:
7447:
7445:
7438:
7434:
7422:
7417:
7414:
7409:
7405:
7401:
7396:
7394:
7387:
7383:
7371:
7370:
7369:
7367:
7363:
7353:
7335:
7329:
7326:
7322:
7318:
7315:
7311:
7307:
7301:
7296:
7293:
7285:
7282:
7279:
7273:
7263:
7262:
7261:
7244:
7237:
7232:
7228:
7224:
7220:
7211:
7206:
7203:
7200:
7196:
7192:
7188:
7179:
7175:
7170:
7167:
7163:
7159:
7155:
7145:
7144:
7143:
7141:
7136:
7134:
7109:
7103:
7096:
7091:
7087:
7082:
7079:
7074:
7070:
7060:
7059:
7058:
7056:
7052:
7028:
7024:
7017:
7013:
7009:
7004:
7000:
6997:
6994:
6990:
6982:
6974:
6971:
6968:
6961:
6956:
6952:
6949:
6942:
6941:
6940:
6938:
6934:
6930:
6920:
6918:
6913:
6894:
6891:
6883:
6877:
6874:
6866:
6863:
6859:
6850:
6846:
6838:
6837:
6836:
6834:
6829:
6827:
6807:
6799:
6795:
6789:
6785:
6779:
6776:
6772:
6768:
6765:
6759:
6753:
6748:
6736:
6735:
6734:
6732:
6711:
6704:
6698:
6695:
6689:
6683:
6675:
6671:
6663:
6662:
6661:
6659:
6655:
6652:
6648:
6643:
6641:
6637:
6627:
6625:
6621:
6602:
6597:
6587:
6583:
6579:
6576:
6568:
6563:
6559:
6556:
6553:
6543:
6542:
6541:
6521:
6517:
6512:
6507:
6504:
6499:
6496:
6489:
6488:
6487:
6482:
6478:
6459:
6451:
6448:
6441:
6438:
6435:
6431:
6425:
6422:
6419:
6413:
6408:
6404:
6396:
6395:
6394:
6392:
6384:
6382:
6358:
6355:
6350:
6346:
6341:
6338:
6331:
6330:
6329:
6327:
6322:
6320:
6310:
6308:
6288:
6283:
6280:
6275:
6271:
6268:
6265:
6260:
6256:
6248:
6247:
6246:
6244:
6226:
6221:
6218:
6213:
6208:
6205:
6200:
6197:
6190:
6189:
6188:
6186:
6182:
6159:
6155:
6149:
6145:
6137:
6134:
6129:
6123:
6117:
6114:
6107:
6106:
6105:
6103:
6099:
6088:
6085:
6077:
6074:December 2019
6067:
6063:
6059:
6053:
6052:
6048:
6043:This section
6041:
6037:
6032:
6031:
6023:
6021:
6017:
6013:
6009:
5985:
5981:
5977:
5971:
5966:
5962:
5959:
5954:
5951:
5945:
5941:
5934:
5930:
5924:
5920:
5915:
5912:
5907:
5903:
5900:
5893:
5892:
5891:
5871:
5866:
5862:
5855:
5850:
5846:
5843:
5838:
5835:
5829:
5825:
5818:
5814:
5808:
5803:
5799:
5791:
5790:
5789:
5787:
5783:
5773:
5771:
5767:
5763:
5753:
5751:
5747:
5727:
5721:
5718:
5713:
5710:
5706:
5702:
5699:
5696:
5689:
5688:
5687:
5685:
5661:
5656:
5652:
5648:
5643:
5639:
5635:
5628:
5627:
5626:
5624:
5619:
5617:
5613:
5606:
5587:
5581:
5576:
5572:
5568:
5565:
5562:
5557:
5552:
5548:
5538:
5537:
5536:
5533:
5531:
5527:
5523:
5504:
5500:
5494:
5490:
5484:
5481:
5476:
5473:
5469:
5465:
5462:
5459:
5456:
5449:
5448:
5447:
5445:
5441:
5437:
5427:
5425:
5421:
5398:
5395:
5390:
5387:
5384:
5380:
5368:
5360:
5358:
5351:
5348:
5345:
5341:
5335:
5329:
5317:
5314:
5309:
5306:
5303:
5299:
5287:
5279:
5277:
5270:
5267:
5264:
5260:
5254:
5248:
5231:
5229:
5222:
5219:
5216:
5212:
5206:
5200:
5184:
5183:
5182:
5179:
5177:
5173:
5169:
5165:
5161:
5157:
5135:
5132:
5129:
5126:
5121:
5118:
5115:
5109:
5104:
5101:
5098:
5094:
5086:
5085:
5084:
5082:
5078:
5073:
5071:
5052:
5049:
5046:
5036:
5033:
5030:
5019:
5016:
5013:
5010:
5007:
5002:
4999:
4996:
4990:
4985:
4982:
4979:
4975:
4967:
4966:
4965:
4960:
4955:
4934:
4931:
4928:
4917:
4909:
4907:
4902:
4897:
4891:
4879:
4876:
4873:
4862:
4854:
4852:
4847:
4842:
4836:
4819:
4817:
4812:
4807:
4801:
4785:
4784:
4783:
4780:
4778:
4774:
4770:
4766:
4762:
4758:
4736:
4733:
4730:
4727:
4722:
4719:
4716:
4710:
4707:
4700:
4699:
4698:
4697:
4693:
4688:
4686:
4667:
4664:
4661:
4651:
4648:
4645:
4634:
4631:
4628:
4625:
4622:
4617:
4614:
4611:
4605:
4602:
4595:
4594:
4593:
4591:
4587:
4583:
4574:
4566:
4558:
4550:
4540:
4537:
4529:
4526:December 2019
4519:
4515:
4511:
4505:
4504:
4500:
4495:This section
4493:
4489:
4484:
4483:
4475:
4472:
4468:
4463:
4461:
4456:
4451:
4449:
4445:
4441:
4436:
4434:
4430:
4426:
4422:
4417:
4414:
4410:
4405:
4364:
4362:
4358:
4354:
4350:
4346:
4342:
4338:
4328:
4326:
4322:
4317:
4315:
4311:
4307:
4303:
4299:
4295:
4291:
4287:
4283:
4279:
4272:
4268:
4264:
4259:
4255:
4253:
4249:
4244:
4241:
4235:
4229:
4224:
4220:
4216:
4212:
4208:
4204:
4199:
4196:
4190:
4184:
4179:
4175:
4172:
4168:
4164:
4160:
4155:
4153:
4149:
4145:
4141:
4137:
4133:
4129:
4125:
4121:
4116:
4114:
4110:
4106:
4096:
4094:
4084:
4079:
4072:
4065:
4061:
4060:optical power
4054:
4047:
4040:
4035:
4033:
4029:
4025:
4017:
3999:
3981:
3968:
3964:
3961:As for other
3954:
3951:
3948:
3946:
3942:
3938:
3934:
3930:
3926:
3921:
3920:in parallel.
3919:
3915:
3911:
3907:
3903:
3899:
3895:
3891:
3885:
3875:
3873:
3868:
3857:
3854:
3846:
3843:December 2019
3836:
3832:
3828:
3822:
3821:
3817:
3812:This section
3810:
3806:
3801:
3800:
3792:
3786:
3772:
3769:
3765:
3761:
3757:
3753:
3749:
3744:
3739:
3731:
3719:
3711:
3684:
3682:
3678:
3674:
3670:
3666:
3662:
3657:
3647:
3629:
3595:
3587:
3575:
3567:
3554:
3526:
3524:
3520:
3516:
3512:
3508:
3504:
3500:
3496:
3489:Average speed
3476:
3459:
3454:
3451:
3446:
3438:
3434:
3428:
3423:
3420:
3417:
3405:
3402:
3397:
3393:
3387:
3383:
3377:
3372:
3369:
3366:
3355:
3350:
3340:
3336:
3330:
3326:
3318:
3313:
3310:
3307:
3295:
3291:
3285:
3280:
3277:
3274:
3263:
3260:
3253:
3252:
3251:
3249:
3231:
3227:
3204:
3200:
3177:
3173:
3150:
3146:
3138:
3127:
3124:
3116:
3113:December 2019
3106:
3102:
3098:
3092:
3091:
3087:
3082:This section
3080:
3076:
3071:
3070:
3048:
3043:
3038:
3032:
3029:
3024:
3021:
3017:
3010:
3007:
3002:
2999:
2996:
2989:
2985:
2979:
2975:
2969:
2962:
2958:
2952:
2948:
2938:
2937:
2936:
2934:
2930:
2926:
2922:
2903:
2895:
2891:
2885:
2881:
2877:
2872:
2868:
2862:
2858:
2854:
2849:
2845:
2839:
2835:
2827:
2823:
2817:
2813:
2807:
2803:
2799:
2793:
2790:
2783:
2782:
2781:
2765:
2761:
2738:
2734:
2711:
2707:
2695:Three numbers
2692:
2676:
2673:
2668:
2665:
2657:
2653:
2649:
2645:
2641:
2625:
2622:
2616:
2613:
2587:
2583:
2578:
2575:
2570:
2566:
2563:
2558:
2553:
2549:
2543:
2540:
2533:
2532:
2531:
2517:
2510:
2506:
2500:
2496:
2490:
2487:
2480:
2462:
2456:
2452:
2448:
2443:
2439:
2432:
2429:
2422:
2403:
2398:
2389:
2385:
2380:
2376:
2370:
2362:
2358:
2353:
2349:
2340:
2335:
2332:
2303:
2299:
2295:
2290:
2286:
2278:
2274:
2268:
2264:
2260:
2254:
2251:
2244:
2243:
2242:
2226:
2222:
2199:
2195:
2182:
2177:
2173:
2169:
2165:
2160:
2141:
2138:
2135:
2132:
2129:
2126:
2123:
2115:
2111:
2107:
2103:
2099:
2095:
2091:
2087:
2083:
2079:
2075:
2071:
2066:
2051:
2048:
2040:
2037:December 2019
2030:
2026:
2022:
2016:
2015:
2011:
2006:This section
2004:
2000:
1995:
1994:
1986:
1984:
1979:
1966:
1959:
1952:
1948:
1942:
1937:
1934:
1931:
1918:
1914:
1910:
1905:
1902:
1899:
1893:
1889:
1883:
1878:
1875:
1872:
1859:
1855:
1851:
1846:
1840:
1836:
1830:
1825:
1822:
1819:
1806:
1802:
1798:
1792:
1788:
1782:
1777:
1772:
1766:
1762:
1758:
1755:
1752:
1747:
1743:
1738:
1734:
1730:
1723:
1716:
1710:
1707:
1704:
1700:
1696:
1691:
1687:
1681:
1677:
1673:
1670:
1667:
1662:
1658:
1654:
1649:
1645:
1639:
1635:
1631:
1626:
1622:
1618:
1613:
1609:
1603:
1599:
1594:
1590:
1584:
1579:
1574:
1568:
1564:
1560:
1557:
1554:
1549:
1545:
1540:
1536:
1532:
1525:
1521:
1515:
1511:
1507:
1504:
1501:
1496:
1492:
1487:
1483:
1475:
1471:
1467:
1463:
1459:
1455:
1451:
1447:
1442:
1440:
1435:
1431:
1413:
1410:
1405:
1401:
1397:
1394:
1391:
1386:
1383:
1378:
1374:
1370:
1365:
1362:
1357:
1353:
1348:
1343:
1339:
1333:
1329:
1325:
1322:
1319:
1314:
1310:
1306:
1301:
1297:
1292:
1286:
1283:
1279:
1275:
1271:
1265:
1261:
1257:
1254:
1251:
1246:
1242:
1238:
1233:
1229:
1224:
1220:
1212:
1205:
1200:
1197:
1193:
1189:
1185:
1178:
1174:
1168:
1164:
1160:
1153:
1149:
1148:harmonic mean
1142:
1138:
1131:
1127:
1120:
1116:
1109:
1105:
1098:
1094:
1090:
1085:
1080:
1071:
1069:
1064:
1062:
1041:
1037:
1033:
1028:
1024:
1014:
1011:
1003:
999:
995:
990:
986:
979:
976:
968:
964:
960:
955:
951:
936:
935:Schur-concave
931:
918:
913:
909:
903:
898:
895:
892:
888:
881:
878:
872:
864:
860:
856:
853:
850:
845:
841:
837:
832:
828:
821:
794:
787:
779:
775:
771:
766:
763:
756:
752:
748:
743:
736:
732:
728:
722:
718:
714:
709:
707:
697:
693:
689:
686:
683:
678:
674:
670:
665:
661:
654:
647:
640:
632:
628:
624:
619:
616:
609:
605:
601:
596:
589:
585:
581:
575:
571:
567:
562:
560:
550:
546:
542:
539:
536:
531:
527:
523:
518:
514:
507:
496:
495:
494:
492:
473:
463:
459:
455:
448:
443:
440:
437:
433:
428:
423:
413:
409:
405:
400:
397:
394:
387:
383:
379:
374:
367:
363:
359:
353:
348:
340:
336:
332:
329:
326:
321:
317:
313:
308:
304:
297:
290:
289:
288:
272:
268:
264:
261:
258:
253:
249:
245:
240:
236:
228:
224:
200:
196:
193:
188:
185:
180:
172:
169:
164:
159:
156:
151:
146:
143:
137:
132:
127:
124:
119:
114:
108:
105:
101:
97:
92:
89:
85:
81:
76:
73:
69:
62:
53:
52:
51:
49:
45:
40:
38:
34:
30:
26:
25:harmonic mean
22:
11476:
11464:
11445:
11438:
11350:Econometrics
11300: /
11283:Chemometrics
11260:Epidemiology
11253: /
11226:Applications
11068:ARIMA model
11015:Q-statistic
10964:Stationarity
10860:Multivariate
10803: /
10799: /
10797:Multivariate
10795: /
10735: /
10731: /
10505:Bayes factor
10404:Signed rank
10316:
10290:
10282:
10270:
9965:Completeness
9801:Cohort study
9699:Opinion poll
9634:Missing data
9621:Study design
9576:Scatter plot
9498:Scatter plot
9491:Spearman's Ļ
9453:Grouped data
9289:
9159:cut-the-knot
9144:
9118:
9109:
9084:. Retrieved
9077:the original
9049:
9033:
9024:
9003:
8994:
8978:
8969:
8960:
8939:
8930:
8921:
8907:
8900:
8892:
8887:
8879:
8812:
8787:
8779:
8746:
8742:
8736:
8717:
8711:
8688:
8682:
8670:. Retrieved
8666:the original
8661:
8652:
8640:. Retrieved
8631:
8622:
8613:
8587:. Retrieved
8563:
8559:
8549:
8544:
8529:
8524:
8505:
8494:. Retrieved
8490:
8480:
8462:
8443:
8385:
8375:
8361:
8357:
8353:
8349:
8345:
8341:
8336:
8246:
8239:
8226:
8219:
8212:
8205:
8203:
7964:
7962:
7954:
7952:
7799:
7793:
7780:
7778:
7625:
7365:
7361:
7359:
7351:
7259:
7139:
7137:
7130:
7054:
7050:
7048:
6936:
6932:
6928:
6926:
6916:
6914:
6911:
6832:
6830:
6825:
6823:
6730:
6728:
6657:
6653:
6646:
6644:
6639:
6635:
6633:
6617:
6539:
6480:
6476:
6474:
6387:
6385:
6380:
6378:
6325:
6323:
6316:
6306:
6304:
6242:
6241:
6184:
6180:
6178:
6102:delta method
6095:
6080:
6071:
6056:Please help
6044:
6026:Delta method
6019:
6015:
6011:
6007:
6005:
5889:
5785:
5781:
5779:
5759:
5749:
5745:
5743:
5681:
5622:
5620:
5611:
5604:
5602:
5534:
5529:
5525:
5521:
5519:
5443:
5435:
5433:
5423:
5419:
5417:
5180:
5175:
5171:
5167:
5163:
5159:
5155:
5153:
5080:
5076:
5074:
5069:
5067:
4958:
4956:
4953:
4781:
4776:
4772:
4768:
4764:
4760:
4756:
4754:
4695:
4691:
4689:
4684:
4682:
4589:
4585:
4579:
4532:
4523:
4508:Please help
4496:
4464:
4452:
4437:
4421:sabermetrics
4418:
4406:
4365:
4334:
4318:
4313:
4309:
4305:
4301:
4297:
4293:
4289:
4285:
4281:
4275:
4270:
4266:
4262:
4245:
4239:
4233:
4227:
4222:
4214:
4210:
4206:
4202:
4200:
4194:
4188:
4182:
4173:
4166:
4162:
4156:
4151:
4147:
4143:
4139:
4135:
4131:
4124:circumcircle
4117:
4102:
4090:
4077:
4070:
4063:
4052:
4045:
4038:
4036:
4031:
4027:
4023:
4015:
3997:
3979:
3960:
3952:
3949:
3936:
3932:
3928:
3924:
3922:
3909:
3905:
3901:
3893:
3887:
3864:
3849:
3840:
3825:Please help
3813:
3773:
3759:
3755:
3751:
3747:
3745:
3737:
3729:
3717:
3709:
3685:
3680:
3676:
3668:
3664:
3660:
3658:
3645:
3627:
3593:
3585:
3573:
3565:
3552:
3527:
3522:
3518:
3514:
3510:
3506:
3492:
3474:
3247:
3135:If a set of
3134:
3119:
3110:
3095:Please help
3083:
2928:
2924:
2920:
2918:
2698:
2655:
2651:
2647:
2643:
2602:
2418:
2186:
2180:
2171:
2167:
2163:
2101:
2097:
2089:
2081:
2077:
2073:
2043:
2034:
2019:Please help
2007:
1980:
1473:
1469:
1465:
1461:
1457:
1453:
1449:
1445:
1443:
1436:
1432:
1203:
1201:
1187:
1183:
1181:
1176:
1172:
1166:
1162:
1158:
1151:
1147:
1140:
1129:
1118:
1107:
1096:
1092:
1088:
1065:
932:
813:
488:
227:real numbers
222:
220:
41:
39:is desired.
24:
18:
11478:WikiProject
11393:Cartography
11355:Jurimetrics
11307:Reliability
11038:Time domain
11017:(LjungāBox)
10939:Time-series
10817:Categorical
10801:Time-series
10793:Categorical
10728:(Bernoulli)
10563:Correlation
10543:Correlation
10339:JarqueāBera
10311:Chi-squared
10073:M-estimator
10026:Asymptotics
9970:Sufficiency
9737:Interaction
9649:Replication
9629:Effect size
9586:Violin plot
9566:Radar chart
9546:Forest plot
9536:Correlogram
9486:Kendall's Ļ
4433:stolen base
4099:In geometry
4030:and object
3947:in series.
3878:Electricity
3663:at a speed
2060:Two numbers
1468:. Thus the
21:mathematics
11345:Demography
11063:ARMA model
10868:Regression
10445:(Friedman)
10406:(Wilcoxon)
10344:Normality
10334:Lilliefors
10281:Student's
10157:Resampling
10031:Robustness
10019:divergence
10009:Efficiency
9947:(monotone)
9942:Likelihood
9859:Population
9692:Stratified
9644:Population
9463:Dependence
9419:Count data
9350:Percentile
9327:Dispersion
9260:Arithmetic
9195:Statistics
9086:2012-09-16
8589:2014-09-09
8538:0030730953
8496:2023-05-31
8454:References
8364:= QO = OG.
6475:The mean (
5756:Statistics
4444:bottleneck
4178:hypotenuse
4161:with legs
4122:BC of the
4087:In finance
3941:capacitors
3914:capacitors
3882:See also:
3760:arithmetic
3484:In physics
2110:hypotenuse
2108:. Since a
1211:power mean
1186:data sets
1082:Geometric
217:Definition
44:reciprocal
10726:Logistic
10493:posterior
10419:Rank sum
10167:Jackknife
10162:Bootstrap
9980:Bootstrap
9915:Parameter
9864:Statistic
9659:Statistic
9571:Run chart
9556:Pie chart
9551:Histogram
9541:Fan chart
9516:Bar chart
9398:L-moments
9285:Geometric
9146:MathWorld
8861:−
8845:−
8829:−
8755:0093-3961
8344:and BC =
8107:
8001:
7880:
7823:
7779:Of these
7750:−
7738:
7719:∑
7666:
7653:∑
7582:−
7571:
7532:∑
7493:
7480:∑
7462:
7406:∑
7327:−
7308:
7302:∼
7294:−
7274:
7221:
7204:−
7189:
7180:≥
7168:−
7156:
7104:
7092:≥
7071:
7001:
6975:ϵ
6953:
6892:−
6864:−
6851:∗
6796:μ
6786:σ
6769:μ
6754:
6749:∗
6712:μ
6676:∗
6580:−
6569:∑
6557:−
6513:∑
6479:) of the
6439:≠
6432:∑
6423:−
6351:∑
6319:jackknife
6272:
6214:∑
6118:
6045:does not
5960:−
5942:
5904:
5844:−
5826:
5722:α
5644:∗
5640:μ
5553:∗
5549:μ
5491:σ
5477:−
5474:μ
5466:
5438:) of the
5388:−
5375:∞
5372:→
5369:β
5349:−
5333:→
5330:α
5307:−
5294:∞
5291:→
5288:α
5268:−
5252:→
5249:β
5220:−
5204:→
5201:β
5133:−
5130:β
5119:−
5116:β
5102:−
5047:α
5042:&
5031:β
5017:−
5014:β
5008:α
5000:−
4997:β
4983:−
4924:∞
4921:→
4918:α
4895:→
4892:β
4869:∞
4866:→
4863:β
4840:→
4837:α
4805:→
4802:α
4734:−
4731:α
4720:−
4717:α
4662:β
4657:&
4646:α
4632:−
4629:β
4623:α
4615:−
4612:α
4497:does not
4467:chemistry
4448:gene pool
4409:hydrology
4361:relevance
4349:precision
4252:diagonals
4248:trapezoid
4176:from the
4120:minor arc
4113:altitudes
3945:inductors
3918:inductors
3890:resistors
3814:does not
3779:= 1/speed
3452:−
3414:∑
3403:−
3363:∑
3304:∑
3271:∑
3084:does not
3003:≤
2623:≤
2139:≤
2133:≤
2127:≤
2100:in blue.
2008:does not
1928:∏
1903:…
1869:∏
1816:∏
1756:…
1708:−
1697:⋯
1671:…
1655:⋯
1619:⋯
1558:…
1505:…
1411:−
1395:⋯
1384:−
1363:−
1323:…
1284:−
1255:…
1034:…
1012:≤
996:…
977:≤
961:…
889:∑
854:…
767:…
687:…
620:…
540:…
434:∑
398:⋯
330:…
262:…
125:−
106:−
90:−
74:−
11494:Category
11440:Category
11133:Survival
11010:Johansen
10733:Binomial
10688:Isotonic
10275:(normal)
9920:location
9727:Blocking
9682:Sampling
9561:QāQ plot
9526:Box plot
9508:Graphics
9403:Skewness
9393:Kurtosis
9365:Variance
9295:Heronian
9290:Harmonic
9095:cite web
8913:Archived
8763:41948650
8636:Archived
8598:cite web
8580:Archived
8514:Archived
8470:Archived
8431:GC²
8340:If AC =
8255:See also
5770:infinite
5766:variance
5764:and the
5614:are the
5075:Letting
4690:Letting
4435:totals.
4429:home run
4171:altitude
4109:incircle
4105:triangle
3787:of the s
3752:harmonic
3748:distance
3479:Examples
2650:≤
2477:and the
2176:nomogram
2174:, and a
1184:positive
1182:For all
1161: (
1091: (
11466:Commons
11413:Kriging
11298:Process
11255:studies
11114:Wavelet
10947:General
10114:Plug-in
9908:L space
9687:Cluster
9388:Moments
9206:Outline
8771:2621087
8440:
8428:
8424:
8412:
8408:
8396:
8348:. OC =
7142:> 0
7045:Moments
6939:> 0
6066:removed
6051:sources
5768:may be
4518:removed
4503:sources
4400:
4388:
4382:
4370:
4357:F-score
4321:ellipse
4225:. Then
4103:In any
4020:
4006:
4002:
3988:
3984:
3970:
3835:removed
3820:sources
3795:Density
3742:
3726:
3722:
3706:
3701:
3689:
3655:
3650:
3636:
3632:
3618:
3607:
3603:
3598:
3582:
3578:
3562:
3548:
3543:
3531:
3503:average
3219:, ...,
3165:, ...,
3137:weights
3105:removed
3090:sources
2638:by the
2029:removed
2014:sources
1209:of the
1068:concave
46:of the
29:average
11335:Census
10925:Normal
10873:Manova
10693:Robust
10443:2-way
10435:1-way
10273:-test
9944:
9521:Biplot
9312:Median
9305:Lehmer
9247:Center
8800:
8769:
8761:
8753:
8724:
8699:
8689:Optics
8536:
8467:Course
8390:Using
8366:Using
7953:where
7626:where
7053:and E(
6917:et al.
6915:Akman
6824:where
6624:t test
6379:where
6179:where
6006:where
5744:where
5603:where
5520:where
4353:recall
4323:, the
4319:In an
4312:, and
4246:Let a
4126:of an
3965:, the
3957:Optics
3499:ratios
3246:, the
2927:, and
2603:Since
2322:or
23:, the
11500:Means
10959:Trend
10488:prior
10430:anova
10319:-test
10293:-test
10285:-test
10192:Power
10137:Pivot
9930:shape
9925:scale
9375:Shape
9355:Range
9300:Heinz
9275:Cubic
9211:Index
9080:(PDF)
9073:(PDF)
8759:JSTOR
8672:8 May
8642:8 May
8583:(PDF)
8576:(PDF)
8328:Notes
8236:Notes
6733:) is
5178:ā ā.
4962:1 ā X
4779:ā ā.
4402:= 4.8
4397:6 + 4
4391:2Ā·6Ā·4
4379:6 + 4
4213:>
4157:In a
3867:alloy
3710:xt+yt
3495:rates
2183:axis.
1439:below
1156:>
1145:>
1134:>
1123:>
1101:>
1086:that
11192:Test
10392:Sign
10244:Wald
9317:Mode
9255:Mean
9101:link
8798:ISBN
8767:SSRN
8751:ISSN
8722:ISBN
8697:ISBN
8674:2018
8644:2018
8604:link
8534:ISBN
8356:and
8240:The
7970:are
7820:bias
7805:are
7796:bias
6995:<
6645:Let
6305:and
6049:any
6047:cite
5762:mean
5610:and
5524:and
5050:>
5034:>
4665:>
4649:>
4592:is:
4588:and
4501:any
4499:cite
4469:and
4431:and
4343:and
4300:and
4269:and
4237:and
4205:and
4201:Let
4192:and
4169:and
4165:and
4150:and
4134:and
4069:and
4044:and
3935:and
3927:and
3908:and
3818:any
3816:cite
3756:time
3679:and
3661:time
3521:and
3497:and
3088:any
3086:cite
2753:and
2214:and
2170:and
2076:and
2012:any
2010:cite
1175:and
37:rate
10372:BIC
10367:AIC
9157:at
9039:doi
8984:doi
8878:,"
8794:172
8352:of
8098:log
7992:log
7877:Var
7729:log
7657:log
7568:exp
7484:log
7459:exp
6998:Var
6950:Var
6927:If
6656:*(
6269:Var
6115:Var
6060:by
5901:Var
5686:is
5463:exp
5446:is
5365:lim
5326:lim
5284:lim
5245:lim
5197:lim
4914:lim
4888:lim
4859:lim
4833:lim
4798:lim
4512:by
4465:In
4438:In
4419:In
4407:In
4373:6Ā·4
4335:In
3829:by
3766:or
3730:x+y
3675:of
3099:by
2530:by
2096:is
2088:is
2023:by
1159:min
1112:or
1108:RMS
1089:max
1018:min
945:min
189:1.5
19:In
11496::
9143:.
9097:}}
9093:{{
9058:^
9012:^
8948:^
8796:.
8765:.
8757:.
8747:36
8745:.
8660:.
8634:.
8630:.
8600:}}
8596:{{
8578:.
8570:,
8489:.
8444:HM
8442:=
8437:OC
8421:OC
8415:GC
8410:=
8405:GC
8399:HC
8394:,
8386:GM
8384:=
8376:QM
8374:=
8350:AM
8232:.
8218:.
7368::
7135:.
6835:)
6638:(
6626:.
6328:)
6317:A
5788:.
5532:.
5422:=
5174:=
5166:=
5158:=
5079:=
4775:=
4767:=
4759:=
4694:=
4308:,
4243:.
4198:.
4154:.
4115:.
4081:am
4056:hm
4004:+
3986:=
3724:=
3718:2t
3704:=
3605:=
3580:+
3546:=
2923:,
2726:,
1213::
1207:ā1
1152:HM
1141:GM
1130:AM
1119:QM
10317:G
10291:F
10283:t
10271:Z
9990:V
9985:U
9187:e
9180:t
9173:v
9149:.
9103:)
9089:.
9041::
8986::
8864:2
8857:d
8853:=
8848:2
8841:b
8837:+
8832:2
8825:a
8806:.
8773:.
8730:.
8705:.
8676:.
8646:.
8608:.
8606:)
8592:.
8568:"
8528:*
8499:.
8446:.
8434:/
8418:/
8402:/
8388:.
8378:.
8362:r
8358:b
8354:a
8346:b
8342:a
8230:1
8227:H
8223:2
8220:H
8216:1
8213:H
8209:3
8206:H
8184:]
8178:4
8172:2
8167:v
8163:C
8159:+
8156:1
8150:+
8147:1
8143:[
8137:n
8132:)
8126:v
8122:C
8118:+
8115:1
8111:(
8102:e
8094:H
8083:]
8077:2
8071:2
8066:v
8062:C
8058:+
8055:1
8049:+
8046:1
8042:[
8035:n
8032:2
8026:)
8020:v
8016:C
8012:+
8009:1
8005:(
7996:e
7988:H
7968:3
7965:H
7958:v
7955:C
7932:n
7926:v
7922:C
7916:2
7912:H
7905:=
7897:]
7892:1
7888:H
7884:[
7868:n
7862:v
7858:C
7854:H
7848:=
7840:]
7835:1
7831:H
7827:[
7803:1
7800:H
7784:3
7781:H
7762:2
7757:)
7753:m
7747:)
7744:x
7741:(
7733:e
7724:(
7714:n
7711:1
7706:=
7701:2
7697:s
7675:)
7672:x
7669:(
7661:e
7648:n
7645:1
7640:=
7637:m
7606:)
7600:2
7596:s
7590:2
7587:1
7579:m
7575:(
7565:=
7556:3
7552:H
7541:)
7538:x
7535:(
7527:n
7524:1
7516:2
7511:)
7506:]
7502:)
7499:x
7496:(
7488:e
7475:n
7472:1
7466:[
7455:(
7448:=
7439:2
7435:H
7423:)
7418:x
7415:1
7410:(
7402:n
7397:=
7388:1
7384:H
7366:H
7362:x
7336:)
7330:n
7323:X
7319:+
7316:a
7312:(
7305:E
7297:n
7290:)
7286:X
7283:+
7280:a
7277:(
7271:E
7245:.
7238:)
7233:n
7229:X
7225:(
7218:E
7212:)
7207:1
7201:n
7197:X
7193:(
7186:E
7176:)
7171:1
7164:X
7160:(
7153:E
7140:n
7113:)
7110:X
7107:(
7101:E
7097:1
7088:]
7083:X
7080:1
7075:[
7068:E
7055:X
7051:X
7029:.
7025:)
7018:q
7014:X
7010:1
7005:(
6991:]
6983:q
6979:)
6972:+
6969:X
6966:(
6962:1
6957:[
6937:Īµ
6933:q
6929:X
6895:1
6888:)
6884:x
6881:(
6878:E
6875:=
6872:)
6867:1
6860:x
6856:(
6847:E
6833:x
6826:Ļ
6808:]
6800:2
6790:2
6780:+
6777:1
6773:[
6766:=
6763:)
6760:x
6757:(
6745:E
6731:x
6708:)
6705:x
6702:(
6699:f
6696:x
6690:=
6687:)
6684:x
6681:(
6672:f
6658:x
6654:f
6647:Ī¼
6640:x
6636:f
6603:.
6598:2
6593:)
6588:i
6584:w
6577:m
6574:(
6564:n
6560:1
6554:n
6522:i
6518:w
6508:n
6505:1
6500:=
6497:h
6484:i
6481:w
6477:h
6460:.
6452:x
6449:1
6442:i
6436:j
6426:1
6420:n
6414:=
6409:i
6405:w
6390:i
6388:w
6381:x
6359:x
6356:1
6347:n
6342:=
6339:m
6326:m
6307:n
6289:)
6284:x
6281:1
6276:(
6266:=
6261:2
6257:s
6243:s
6227:.
6222:x
6219:1
6209:n
6206:1
6201:=
6198:m
6185:m
6181:H
6160:4
6156:m
6150:2
6146:s
6138:n
6135:1
6130:=
6127:)
6124:H
6121:(
6087:)
6081:(
6076:)
6072:(
6068:.
6054:.
6020:E
6016:n
6012:x
6008:m
5986:2
5982:m
5978:n
5972:]
5967:)
5963:1
5955:x
5952:1
5946:(
5939:E
5935:[
5931:m
5925:=
5921:)
5916:x
5913:1
5908:(
5872:n
5867:2
5863:m
5856:]
5851:)
5847:1
5839:x
5836:1
5830:(
5823:E
5819:[
5815:m
5809:=
5804:2
5800:s
5786:s
5782:m
5750:Ī±
5746:k
5728:)
5719:1
5714:+
5711:1
5707:(
5703:k
5700:=
5697:H
5662:.
5657:2
5653:G
5649:=
5636:H
5623:G
5612:Ī¼
5608:v
5605:C
5588:,
5582:2
5577:v
5573:C
5569:+
5566:1
5563:=
5558:H
5530:X
5526:Ļ
5522:Ī¼
5505:,
5501:)
5495:2
5485:2
5482:1
5470:(
5460:=
5457:H
5444:X
5436:H
5424:Ī²
5420:Ī±
5399:1
5396:=
5391:X
5385:1
5381:H
5361:=
5352:X
5346:1
5342:H
5336:0
5318:0
5315:=
5310:X
5304:1
5300:H
5280:=
5271:X
5265:1
5261:H
5255:1
5232:=
5223:X
5217:1
5213:H
5207:0
5176:Ī²
5172:Ī±
5168:Ī²
5164:Ī±
5160:Ī²
5156:Ī±
5136:1
5127:2
5122:1
5110:=
5105:X
5099:1
5095:H
5081:Ī²
5077:Ī±
5070:Ī²
5053:0
5037:1
5020:1
5011:+
5003:1
4991:=
4986:X
4980:1
4976:H
4959:H
4935:1
4932:=
4929:H
4910:=
4903:H
4898:0
4880:0
4877:=
4874:H
4855:=
4848:H
4843:1
4820:=
4813:H
4808:0
4777:Ī²
4773:Ī±
4769:Ī²
4765:Ī±
4761:Ī²
4757:Ī±
4737:1
4728:2
4723:1
4711:=
4708:H
4696:Ī²
4692:Ī±
4685:Ī±
4668:0
4652:1
4635:1
4626:+
4618:1
4606:=
4603:H
4590:Ī²
4586:Ī±
4539:)
4533:(
4528:)
4524:(
4520:.
4506:.
4394:/
4376:/
4314:h
4310:B
4306:A
4302:B
4298:A
4294:h
4290:h
4286:B
4282:A
4271:B
4267:A
4263:h
4240:t
4234:c
4228:s
4223:c
4215:s
4211:t
4209:(
4207:s
4203:t
4195:b
4189:a
4183:h
4174:h
4167:b
4163:a
4152:t
4148:q
4144:y
4140:y
4136:t
4132:q
4078:P
4074:2
4071:P
4067:1
4064:P
4053:f
4049:2
4046:f
4042:1
4039:f
4032:v
4028:u
4024:f
4016:v
4012:/
4009:1
3998:u
3994:/
3991:1
3980:f
3976:/
3973:1
3937:y
3933:x
3929:y
3925:x
3910:y
3906:x
3902:y
3898:Ī©
3894:x
3856:)
3850:(
3845:)
3841:(
3837:.
3823:.
3789:i
3781:i
3777:i
3738:2
3734:/
3714:/
3695:/
3681:y
3677:x
3669:y
3665:x
3646:y
3642:/
3639:1
3634:+
3628:x
3624:/
3621:1
3613:/
3610:2
3594:y
3590:/
3586:d
3574:x
3570:/
3566:d
3557:/
3553:d
3551:2
3537:/
3523:y
3519:x
3515:y
3511:x
3507:d
3460:.
3455:1
3447:)
3439:i
3435:w
3429:n
3424:1
3421:=
3418:i
3406:1
3398:i
3394:x
3388:i
3384:w
3378:n
3373:1
3370:=
3367:i
3356:(
3351:=
3341:i
3337:x
3331:i
3327:w
3319:n
3314:1
3311:=
3308:i
3296:i
3292:w
3286:n
3281:1
3278:=
3275:i
3264:=
3261:H
3232:n
3228:x
3205:1
3201:x
3178:n
3174:w
3151:1
3147:w
3126:)
3120:(
3115:)
3111:(
3107:.
3093:.
3049:.
3044:2
3039:)
3033:H
3030:A
3025:+
3022:1
3018:(
3011:4
3008:3
3000:1
2997:+
2990:3
2986:H
2980:3
2976:G
2970:+
2963:3
2959:G
2953:3
2949:A
2929:A
2925:G
2921:H
2904:.
2896:3
2892:x
2886:2
2882:x
2878:+
2873:3
2869:x
2863:1
2859:x
2855:+
2850:2
2846:x
2840:1
2836:x
2828:3
2824:x
2818:2
2814:x
2808:1
2804:x
2800:3
2794:=
2791:H
2766:3
2762:x
2739:2
2735:x
2712:1
2708:x
2677:H
2674:A
2669:=
2666:G
2656:n
2652:G
2648:H
2644:n
2626:1
2617:A
2614:G
2588:.
2584:)
2579:A
2576:G
2571:(
2567:G
2564:=
2559:A
2554:2
2550:G
2544:=
2541:H
2518:,
2511:2
2507:x
2501:1
2497:x
2491:=
2488:G
2463:2
2457:2
2453:x
2449:+
2444:1
2440:x
2433:=
2430:A
2404:.
2399:2
2395:)
2390:2
2386:x
2381:/
2377:1
2374:(
2371:+
2368:)
2363:1
2359:x
2354:/
2350:1
2347:(
2341:=
2336:H
2333:1
2304:2
2300:x
2296:+
2291:1
2287:x
2279:2
2275:x
2269:1
2265:x
2261:2
2255:=
2252:H
2227:2
2223:x
2200:1
2196:x
2181:z
2172:y
2168:x
2164:z
2154:.
2142:Q
2136:A
2130:G
2124:H
2102:Q
2098:G
2090:A
2082:H
2078:b
2074:a
2050:)
2044:(
2039:)
2035:(
2031:.
2017:.
1967:.
1960:)
1953:i
1949:x
1943:n
1938:1
1935:=
1932:i
1919:n
1915:x
1911:1
1906:,
1900:,
1894:i
1890:x
1884:n
1879:1
1876:=
1873:i
1860:2
1856:x
1852:1
1847:,
1841:i
1837:x
1831:n
1826:1
1823:=
1820:i
1807:1
1803:x
1799:1
1793:(
1789:A
1783:n
1778:)
1773:)
1767:n
1763:x
1759:,
1753:,
1748:1
1744:x
1739:(
1735:G
1731:(
1724:=
1717:)
1711:1
1705:n
1701:x
1692:2
1688:x
1682:1
1678:x
1674:,
1668:,
1663:n
1659:x
1650:3
1646:x
1640:1
1636:x
1632:,
1627:n
1623:x
1614:3
1610:x
1604:2
1600:x
1595:(
1591:A
1585:n
1580:)
1575:)
1569:n
1565:x
1561:,
1555:,
1550:1
1546:x
1541:(
1537:G
1533:(
1526:=
1522:)
1516:n
1512:x
1508:,
1502:,
1497:1
1493:x
1488:(
1484:H
1474:n
1470:n
1466:n
1462:n
1458:n
1454:n
1450:j
1446:n
1414:1
1406:n
1402:x
1398:+
1392:+
1387:1
1379:2
1375:x
1371:+
1366:1
1358:1
1354:x
1349:n
1344:=
1340:)
1334:n
1330:x
1326:,
1320:,
1315:2
1311:x
1307:,
1302:1
1298:x
1293:(
1287:1
1280:M
1276:=
1272:)
1266:n
1262:x
1258:,
1252:,
1247:2
1243:x
1239:,
1234:1
1230:x
1225:(
1221:H
1204:M
1177:b
1173:a
1169:)
1167:b
1165:,
1163:a
1154:)
1150:(
1143:)
1139:(
1132:)
1128:(
1121:)
1117:(
1110:)
1106:(
1099:)
1097:b
1095:,
1093:a
1047:)
1042:n
1038:x
1029:1
1025:x
1021:(
1015:n
1009:)
1004:n
1000:x
991:1
987:x
983:(
980:H
974:)
969:n
965:x
956:1
952:x
948:(
919:.
914:i
910:x
904:n
899:1
896:=
893:i
882:n
879:1
873:=
870:)
865:n
861:x
857:,
851:,
846:2
842:x
838:,
833:1
829:x
825:(
822:A
795:,
788:)
780:n
776:x
772:1
764:,
757:2
753:x
749:1
744:,
737:1
733:x
729:1
723:(
719:H
715:1
710:=
703:)
698:n
694:x
690:,
684:,
679:2
675:x
671:,
666:1
662:x
658:(
655:A
648:,
641:)
633:n
629:x
625:1
617:,
610:2
606:x
602:1
597:,
590:1
586:x
582:1
576:(
572:A
568:1
563:=
556:)
551:n
547:x
543:,
537:,
532:2
528:x
524:,
519:1
515:x
511:(
508:H
474:.
464:i
460:x
456:1
449:n
444:1
441:=
438:i
429:n
424:=
414:n
410:x
406:1
401:+
395:+
388:2
384:x
380:1
375:+
368:1
364:x
360:1
354:n
349:=
346:)
341:n
337:x
333:,
327:,
322:2
318:x
314:,
309:1
305:x
301:(
298:H
273:n
269:x
265:,
259:,
254:2
250:x
246:,
241:1
237:x
223:H
201:.
197:2
194:=
186:3
181:=
173:4
170:1
165:+
160:4
157:1
152:+
147:1
144:1
138:3
133:=
128:1
120:)
115:3
109:1
102:4
98:+
93:1
86:4
82:+
77:1
70:1
63:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
