9892:
12647:
20:
12633:
9736:
9140:
8824:
12671:
4306:
12659:
9184:
8883:
8575:
3929:
9731:{\displaystyle {\begin{aligned}P(X_{(k)}=x)&=P(X_{(k)}\leq x)-P(X_{(k)}<x),\\&=\sum _{j=0}^{n-k}{n \choose j}\left(p_{3}^{j}(p_{1}+p_{2})^{n-j}-(p_{2}+p_{3})^{j}(p_{1})^{n-j}\right),\\&=\sum _{j=0}^{n-k}{n \choose j}\left((1-F(x))^{j}(F(x))^{n-j}-(1-F(x)+f(x))^{j}(F(x)-f(x))^{n-j}\right).\end{aligned}}}
8183:
based approaches, the tuning parameter for the order statistic based density estimator is the size of sample subsets. Such an estimator is more robust than histogram and kernel based approaches, for example densities like the Cauchy distribution (which lack finite moments) can be inferred without the
6052:
With such a small sample size, if one wants at least 95% confidence, one is reduced to saying that the median is between the minimum and the maximum of the 6 observations with probability 31/32 or approximately 97%. Size 6 is, in fact, the smallest sample size such that the interval determined by the
5798:
As an example, consider a random sample of size 6. In that case, the sample median is usually defined as the midpoint of the interval delimited by the 3rd and 4th order statistics. However, we know from the preceding discussion that the probability that this interval actually contains the population
9760:
th smallest (or largest) element of a list is called the selection problem and is solved by a selection algorithm. Although this problem is difficult for very large lists, sophisticated selection algorithms have been created that can solve this problem in time proportional to the number of elements
5897:
of the population median, what this example illustrates is that it is not a particularly good one in absolute terms. In this particular case, a better confidence interval for the median is the one delimited by the 2nd and 5th order statistics, which contains the population median with probability
9135:{\displaystyle {\begin{aligned}P(X_{(k)}<x)&=P({\text{there are at least }}k{\text{ observations less than }}x),\\&=P({\text{there are at most }}n-k{\text{ observations greater than or equal to }}x),\\&=\sum _{j=0}^{n-k}{n \choose j}(p_{2}+p_{3})^{j}(p_{1})^{n-j}.\end{aligned}}}
8819:{\displaystyle {\begin{aligned}P(X_{(k)}\leq x)&=P({\text{there are at least }}k{\text{ observations less than or equal to }}x),\\&=P({\text{there are at most }}n-k{\text{ observations greater than }}x),\\&=\sum _{j=0}^{n-k}{n \choose j}p_{3}^{j}(p_{1}+p_{2})^{n-j}.\end{aligned}}}
4301:{\displaystyle \operatorname {Var} (U_{(k)}-U_{(j)})=\operatorname {Var} (U_{(k)})+\operatorname {Var} (U_{(j)})-2\cdot \operatorname {Cov} (U_{(k)},U_{(j)})={\frac {k(n-k+1)}{(n+1)^{2}(n+2)}}+{\frac {j(n-j+1)}{(n+1)^{2}(n+2)}}-2\cdot \operatorname {Cov} (U_{(k)},U_{(j)})}
7214:
2929:
4735:
5518:
8537:
5711:
1679:
1519:
6348:
3924:
8039:
4434:
3345:
6171:
1368:
8135:
5178:
6513:
2627:
614:
6629:
3788:
2167:
1156:
2255:
265:
5888:
10231:
M. Cardone, A. Dytso and C. Rush, "Entropic
Central Limit Theorem for Order Statistics," in IEEE Transactions on Information Theory, vol. 69, no. 4, pp. 2193-2205, April 2023, doi: 10.1109/TIT.2022.3219344.
4508:
6047:
490:
380:
6894:
7577:
5773:
7516:
9189:
8888:
8580:
3414:
6968:
2691:
1713:
family. We also give a simple method to derive the joint distribution of any number of order statistics, and finally translate these results to arbitrary continuous distributions using the
7340:
7418:
8253:
1777:
7624:
7032:
4619:
5186:
4858:
1982:
4578:
6788:
1910:
3630:
1864:
7664:
8875:
4961:
3793:
3682:
3592:
8188:. This is because the first moment of the order statistic always exists if the expected value of the underlying distribution does, but the converse is not necessarily true.
8567:
8341:
3488:
3458:
7857:
7812:
385:
where, following a common convention, we use upper-case letters to refer to random variables, and lower-case letters (as above) to refer to their actual observed values.
8349:
8171:
7890:
7777:
7456:
4903:
7917:
5552:
4311:
2971:
2362:
1527:
786:
694:
3187:
3146:
3105:
3064:
2488:
2447:
978:
9176:
7004:
5544:
2291:
2018:
1379:
747:
7694:
7748:
7721:
7264:
6725:
6698:
3023:
2406:
1808:
8314:
8282:
3514:
6194:
3537:
7937:
7367:
7237:
7024:
6388:
An interesting observation can be made in the case where the distribution is symmetric, and the population median equals the population mean. In this case, the
6381:
representation which provides information about the errorbounds. The convergence to normal distribution also holds in a stronger sense, such as convergence in
6673:
Moments of the distribution for the first order statistic can be used to develop a non-parametric density estimator. Suppose, we want to estimate the density
3687:
788:, and the sample median is some function of the two (usually the average) and hence not an order statistic. Similar remarks apply to all sample quantiles.
9761:
in the list, even if the list is totally unordered. If the data is stored in certain specialized data structures, this time can be brought down to O(log
7946:
3206:
6079:
1167:
8044:
4980:
6426:
2500:
11768:
505:
6524:
2026:
12273:
990:
2186:
134:
12423:
3192:
One reasons in an entirely analogous way to derive the higher-order joint distributions. Perhaps surprisingly, the joint density of the
12047:
10688:
10160:
Hlynka, M.; Brill, P. H.; Horn, W. (2010). "A method for obtaining
Laplace transforms of order statistics of Erlang random variables".
3420:
that the maximum expected number of uniform U(0,1] random variables one can choose from a sample of size n with a sum up not exceeding
5805:
11821:
3354:! different permutations of the sample corresponding to the same sequence of order statistics. This is related to the fact that 1/
12260:
886:
4439:
5904:
416:
309:
6793:
3542:
Using the above formulas, one can derive the distribution of the range of the order statistics, that is the distribution of
10683:
10383:
7524:
5716:
120:
For example, suppose that four numbers are observed or recorded, resulting in a sample of size 4. If the sample values are
7461:
11287:
10435:
3361:
2924:{\displaystyle f_{U_{(i)},U_{(j)}}(u,v)=n!{u^{i-1} \over (i-1)!}{(v-u)^{j-i-1} \over (j-i-1)!}{(1-v)^{n-j} \over (n-j)!}}
921:
101:
6899:
3416:. It is also related with another particularity of order statistics of uniform random variables: It follows from the
12697:
12070:
11962:
10307:
10196:
10107:
10036:
10006:
9979:
9935:
9913:
1913:
1698:
109:
9906:
12675:
12248:
12122:
7269:
1714:
105:
3350:
One way to understand this is that the unordered sample does have constant density equal to 1, and that there are
630:
The sample median may or may not be an order statistic, since there is a single middle value only when the number
12306:
11967:
11712:
11083:
10673:
9806:
7372:
6382:
7209:{\displaystyle E(Y_{(1)})={\frac {1}{(N+1)g(0)}}+{\frac {1}{(N+1)(N+2)}}\int _{0}^{1}Q''(z)\delta _{N+1}(z)\,dz}
4730:{\displaystyle X_{(i)}{\stackrel {d}{=}}{\frac {1}{\lambda }}\left(\sum _{j=1}^{i}{\frac {Z_{j}}{n-j+1}}\right)}
12357:
11569:
11376:
11265:
11223:
10052:
Jones, M. C. (2009), "Kumaraswamy's distribution: A beta-type distribution with some tractability advantages",
8199:
5513:{\displaystyle f_{X_{(j)},X_{(k)}}(x,y)={\frac {n!}{(j-1)!(k-j-1)!(n-k)!}}^{j-1}^{k-1-j}^{n-k}f_{X}(x)f_{X}(y)}
4751:
are iid standard exponential random variables (i.e. with rate parameter 1). This result was first published by
2660:
1723:
910:
11297:
7582:
12600:
11559:
10462:
4795:
1919:
12151:
12100:
12085:
12075:
11944:
11816:
11783:
11609:
11564:
11394:
925:
23:
4774:
4521:
12702:
12663:
12495:
12296:
12220:
11521:
11275:
10944:
10408:
6730:
1869:
3597:
1813:
12380:
12352:
12347:
12095:
11854:
11760:
11740:
11648:
11359:
11177:
10660:
10532:
10131:
9880:
9845:
7629:
12112:
11880:
11601:
11526:
11455:
11384:
11304:
11292:
11162:
11150:
11143:
10851:
10572:
10356:
8832:
8285:
8180:
4914:
3635:
3545:
836:
620:
63:
9814:
for the order statistics of independent but not necessarily identically distributed random variables
12595:
12362:
12225:
11910:
11875:
11839:
11624:
11066:
10975:
10934:
10846:
10537:
10376:
9900:
9801:
8545:
8532:{\displaystyle p_{1}=P(X<x)=F(x)-f(x),\ p_{2}=P(X=x)=f(x),{\text{ and }}p_{3}=P(X>x)=1-F(x).}
8319:
6642:
4966:
to derive the following probability density functions for the order statistics of a sample of size
4585:
3463:
3423:
2491:
1161:
the corresponding probability density function may be derived from this result, and is found to be
906:
67:
31:
7823:
7785:
5706:{\displaystyle f_{X_{(1)},\ldots ,X_{(n)}}(x_{1},\ldots ,x_{n})=n!f_{X}(x_{1})\cdots f_{X}(x_{n})}
1674:{\displaystyle F_{X_{(1)}}(x)=\operatorname {Prob} (\min\{\,X_{1},\ldots ,X_{n}\,\}\leq x)=1-^{n}}
12504:
12117:
12057:
11994:
11632:
11616:
11354:
11216:
11206:
11056:
10970:
8147:
7865:
7753:
7423:
6400:
instead. This asymptotic analysis suggests that the mean outperforms the median in cases of low
4866:
1514:{\displaystyle F_{X_{(n)}}(x)=\operatorname {Prob} (\max\{\,X_{1},\ldots ,X_{n}\,\}\leq x)=^{n}}
12542:
12472:
12265:
12202:
11957:
11844:
10841:
10738:
10645:
10524:
10423:
9917:
9860:
9828:
8255:
are i.i.d. random variables from a discrete distribution with cumulative distribution function
8185:
7895:
2937:
2328:
752:
660:
9996:
3151:
3110:
3069:
3028:
2452:
2411:
947:
932:. The peculiarities of the analysis of distributions assigning mass to points (in particular,
499:
is the difference between the maximum and minimum. It is a function of the order statistics:
12707:
12567:
12509:
12452:
12278:
12171:
12080:
11806:
11690:
11549:
11541:
11431:
11423:
11238:
11134:
11112:
11071:
11036:
11003:
10949:
10924:
10879:
10818:
10778:
10580:
10403:
10026:
9811:
9148:
6976:
6661:
are asymptotically normally distributed by the CLT, our results follow by application of the
6393:
5795:
The simplest case to consider is how well the sample median estimates the population median.
5523:
2646:
2263:
1990:
1706:
933:
914:
719:
7669:
12490:
12065:
12014:
11990:
11952:
11870:
11849:
11801:
11680:
11658:
11627:
11536:
11413:
11364:
11282:
11255:
11211:
11167:
10929:
10705:
10585:
9817:
7726:
7699:
7343:
7242:
6703:
6676:
6405:
6343:{\displaystyle X_{(\lceil np\rceil )}\sim AN\left(F^{-1}(p),{\frac {p(1-p)}{n^{2}}}\right)}
2996:
2379:
1786:
703:
637:
59:
8290:
8258:
8:
12637:
12562:
12485:
12166:
11930:
11923:
11885:
11793:
11773:
11745:
11478:
11344:
11339:
11329:
11321:
11139:
11100:
10990:
10980:
10889:
10668:
10624:
10542:
10467:
10369:
10187:
9833:
9747:
6374:
6070:
6053:
minimum and the maximum is at least a 95% confidence interval for the population median.
4789:
4768:
3493:
929:
882:
624:
3919:{\displaystyle \operatorname {Cov} (U_{(k)},U_{(j)})={\frac {j(n-k+1)}{(n+1)^{2}(n+2)}}}
3519:
12651:
12462:
12316:
12212:
12161:
12037:
11934:
11918:
11895:
11672:
11406:
11389:
11349:
11260:
11155:
11117:
11088:
11048:
11008:
10954:
10871:
10557:
10552:
10272:
10254:
7922:
7352:
7222:
7009:
6404:, and vice versa. For example, the median achieves better confidence intervals for the
4775:
The joint distribution of the order statistics of an absolutely continuous distribution
980:, the order statistics for that sample have cumulative distributions as follows (where
93:
51:
5783:
An interesting question is how well the order statistics perform as estimators of the
12646:
12557:
12527:
12519:
12339:
12330:
12255:
12186:
12042:
12027:
12002:
11890:
11831:
11697:
11685:
11311:
11228:
11172:
11095:
10939:
10861:
10640:
10514:
10337:
10303:
10122:
10103:
10032:
10002:
9975:
9766:
9751:
6378:
6366:
4764:
4752:
2177:
1710:
10340:
10276:
12582:
12537:
12301:
12288:
12181:
12156:
12090:
12022:
11900:
11508:
11401:
11334:
11247:
11194:
11013:
10884:
10678:
10562:
10477:
10444:
10295:
10264:
10205:
10169:
10140:
10095:
10061:
9967:
6358:
19:
10191:
8034:{\displaystyle x_{\ell }:d_{\ell }=\sum _{k=1}^{m_{N}}{\frac {d_{\ell k}}{m_{N}}}}
4429:{\displaystyle \operatorname {Var} (U)={\frac {(k-j)(n-(k-j)+1)}{(n+1)^{2}(n+2)}}}
3340:{\displaystyle f_{U_{(1)},U_{(2)},\ldots ,U_{(n)}}(u_{1},u_{2},\ldots ,u_{n})=n!.}
12499:
12243:
12105:
12032:
11707:
11581:
11554:
11531:
11500:
11127:
11122:
10806:
10457:
10268:
10065:
1373:
Moreover, there are two special cases, which have CDFs that are easy to compute.
11989:
10290:
David, H. A.; Nagaraja, H. N. (2003), "Chapter 3. Expected Values and
Moments",
6166:{\displaystyle U_{(\lceil np\rceil )}\sim AN\left(p,{\frac {p(1-p)}{n}}\right).}
12448:
12443:
10906:
10836:
10482:
9796:
5894:
5893:
Although the sample median is probably among the best distribution-independent
3417:
10210:
10173:
10090:
David, H. A.; Nagaraja, H. N. (2003), "Chapter 2. Basic
Distribution Theory",
3790:
From these formulas we can derive the covariance between two order statistics:
1363:{\displaystyle f_{X_{(r)}}(x)={\frac {n!}{(r-1)!(n-r)!}}f_{X}(x)^{r-1}^{n-r}.}
920:
From now on, we will assume that the random variables under consideration are
12691:
12605:
12572:
12435:
12396:
12207:
12176:
11640:
11594:
11199:
10901:
10728:
10492:
10487:
10242:
8130:{\displaystyle x_{\ell }:{\hat {f}}_{\ell }={\frac {1}{2(1+s_{N})d_{\ell }}}}
5173:{\displaystyle f_{X_{(k)}}(x)={\frac {n!}{(k-1)!(n-k)!}}^{k-1}^{n-k}f_{X}(x)}
1780:
1702:
97:
82:
7346:
technique becomes the basis for the following density estimation algorithm,
6508:{\displaystyle B(k,n+1-k)\ {\stackrel {\mathrm {d} }{=}}\ {\frac {X}{X+Y}},}
4513:
12547:
12480:
12457:
12372:
11702:
10998:
10896:
10831:
10773:
10758:
10695:
10650:
10299:
10099:
9765:). In many applications all order statistics are required, in which case a
6662:
2325:. The probability that more than one is in this latter interval is already
496:
2647:
The joint distribution of the order statistics of the uniform distribution
2622:{\displaystyle {n! \over (k-1)!(n-k)!}u^{k-1}\cdot du\cdot (1-u-du)^{n-k}}
12590:
12552:
12235:
12136:
11998:
11811:
11778:
11270:
11187:
11182:
10826:
10783:
10763:
10743:
10733:
10502:
10325:
9822:
6389:
609:{\displaystyle {\rm {Range}}\{\,X_{1},\ldots ,X_{n}\,\}=X_{(n)}-X_{(1)}.}
6624:{\displaystyle X=\sum _{i=1}^{k}Z_{i},\quad Y=\sum _{i=k+1}^{n+1}Z_{i},}
3783:{\displaystyle U_{(k)}-U_{(j)}\sim \operatorname {Beta} (k-j,n-(k-j)+1)}
2162:{\displaystyle f_{U_{(k)}}(u)={n! \over (k-1)!(n-k)!}u^{k-1}(1-u)^{n-k}}
11436:
10916:
10616:
10547:
10497:
10472:
10392:
10329:
10145:
10126:
9971:
9855:
6377:
in his seminal paper in 1946. Further research led in the 1960s to the
4758:
1692:
1151:{\displaystyle F_{X_{(r)}}(x)=\sum _{j=r}^{n}{\binom {n}{j}}^{j}^{n-j}}
939:
39:
2250:{\displaystyle U_{(k)}\sim \operatorname {Beta} (k,n+1\mathbf {-} k).}
260:{\displaystyle x_{(1)}=3,\ \ x_{(2)}=6,\ \ x_{(3)}=7,\ \ x_{(4)}=9,\,}
108:
is used to reduce the analysis to the case of order statistics of the
81:
value of a sample, and (with some qualifications discussed below) the
11589:
11441:
11061:
10856:
10768:
10753:
10748:
10713:
10345:
8176:
11105:
10723:
10600:
10595:
10590:
10070:
As is well known, the beta distribution is the distribution of the
9865:
9850:
9791:
6401:
5784:
905:
can arise by sampling from more than one population. Then they are
889:. This is the case treated below. In general, the random variables
86:
10259:
6396:, is also asymptotically normally distributed, but with variance Ï
5778:
12610:
12311:
6668:
407:
300:
78:
74:
8175:
In contrast to the bandwidth/length based tuning parameters for
5883:{\displaystyle {6 \choose 3}(1/2)^{6}={5 \over 16}\approx 31\%.}
1687:
1684:
Which can be derived by careful consideration of probabilities.
12532:
11513:
11487:
11467:
10718:
10509:
9870:
9786:
6373:. One of the first people to mention and prove this result was
10361:
623:
that is simply related to the order statistics is the sample
924:
and, where convenient, we will also assume that they have a
10452:
9875:
944:
For a random sample as above, with cumulative distribution
62:, order statistics are among the most fundamental tools in
10294:, Wiley Series in Probability and Statistics, p. 34,
7239:
is the quantile function associated with the distribution
4503:{\displaystyle U\sim \operatorname {Beta} (k-j,n-(k-j)+1)}
835:
are also random variables, defined by sorting the values (
10094:, Wiley Series in Probability and Statistics, p. 9,
6042:{\displaystyle \left(1/2)^{6}={25 \over 32}\approx 78\%.}
4514:
Order statistics sampled from an exponential distribution
1697:
In this section we show that the order statistics of the
909:, but not necessarily identically distributed, and their
10335:
8343:
order statistics, three values are first needed, namely
1987:
The probability density function of the order statistic
485:{\displaystyle X_{(n)}=\max\{\,X_{1},\ldots ,X_{n}\,\}.}
73:
Important special cases of the order statistics are the
9178:
is just the difference of these values, that is to say
2364:, so we have to calculate the probability that exactly
2309: â 1 elements of the sample are smaller than
696:
and so is an order statistic. On the other hand, when
375:{\displaystyle X_{(1)}=\min\{\,X_{1},\ldots ,X_{n}\,\}}
6889:{\displaystyle g_{Y}(y)=f_{X}(y+x^{*})+f_{X}(x^{*}-y)}
4510:, which is the actual distribution of the difference.
3594:, i.e. maximum minus the minimum. More generally, for
10245:(2017). "Minimum local distance density estimation".
9187:
9151:
8886:
8835:
8578:
8548:
8352:
8322:
8293:
8261:
8202:
8150:
8047:
7949:
7925:
7898:
7868:
7826:
7788:
7756:
7729:
7702:
7672:
7632:
7585:
7572:{\displaystyle m_{N}=\operatorname {round} (N^{1-a})}
7527:
7464:
7426:
7375:
7355:
7272:
7245:
7225:
7035:
7012:
6979:
6902:
6796:
6733:
6706:
6679:
6527:
6429:
6197:
6082:
5907:
5808:
5768:{\displaystyle x_{1}\leq x_{2}\leq \dots \leq x_{n}.}
5719:
5555:
5526:
5189:
4983:
4917:
4869:
4798:
4622:
4524:
4442:
4314:
3932:
3796:
3690:
3638:
3600:
3548:
3522:
3496:
3466:
3426:
3364:
3209:
3154:
3113:
3072:
3031:
2999:
2940:
2694:
2503:
2455:
2414:
2382:
2331:
2266:
2189:
2029:
1993:
1922:
1872:
1816:
1789:
1726:
1530:
1382:
1170:
993:
950:
755:
722:
663:
508:
419:
312:
137:
12274:
Autoregressive conditional heteroskedasticity (ARCH)
7511:{\displaystyle \{{\hat {f}}_{\ell }\}_{\ell =1}^{M}}
4759:
Order statistics sampled from an Erlang distribution
2176:
th order statistic of the uniform distribution is a
1693:
Order statistics sampled from a uniform distribution
940:
Cumulative distribution function of order statistics
7943:9: Compute the subset average of distances to
3409:{\displaystyle 0<u_{1}<\cdots <u_{n}<1}
11736:
10240:
9730:
9170:
9134:
8869:
8818:
8561:
8531:
8335:
8308:
8276:
8247:
8191:
8165:
8129:
8033:
7931:
7911:
7884:
7851:
7806:
7771:
7742:
7715:
7688:
7658:
7618:
7571:
7510:
7450:
7412:
7361:
7334:
7258:
7231:
7208:
7018:
6998:
6963:{\displaystyle f_{X}(x^{*})={\frac {g_{Y}(0)}{2}}}
6962:
6888:
6782:
6719:
6692:
6623:
6507:
6342:
6165:
6041:
5882:
5767:
5705:
5538:
5512:
5172:
4955:
4897:
4852:
4729:
4572:
4502:
4428:
4300:
3918:
3782:
3676:
3624:
3586:
3531:
3508:
3482:
3452:
3408:
3339:
3181:
3140:
3099:
3058:
3017:
2965:
2923:
2621:
2482:
2441:
2400:
2356:
2285:
2249:
2161:
2012:
1976:
1904:
1858:
1802:
1771:
1673:
1513:
1362:
1150:
972:
780:
741:
688:
608:
484:
374:
259:
10247:Communications in Statistics - Theory and Methods
10074:'th order statistic from a random sample of size
9548:
9535:
9351:
9338:
9054:
9041:
8989: observations greater than or equal to
8746:
8733:
5979:
5966:
5954:
5941:
5929:
5916:
5825:
5812:
2260:The proof of these statements is as follows. For
1066:
1053:
12689:
6973:The expected value of the first order statistic
1575:
1427:
439:
332:
11822:Multivariate adaptive regression splines (MARS)
10159:
10001:(2nd ed.). Cengage Learning. p. 229.
9839:
8569:order statistic can be computed by noting that
7518:estimated density at the points of evaluation.
7420:points of density evaluation. Tuning parameter
5779:Application: confidence intervals for quantiles
9966:. Wiley Series in Probability and Statistics.
8637: observations less than or equal to
6669:Application: Non-parametric density estimation
5790:
1916:. Note that the order statistics also satisfy
1783:drawn from a continuous distribution with cdf
10377:
10289:
10089:
9994:
9961:
9741:
7335:{\displaystyle \delta _{N}(z)=(N+1)(1-z)^{N}}
6790:, which are i.i.d with distribution function
1688:Probability distributions of order statistics
26:of the order statistics for a sample of size
8542:The cumulative distribution function of the
7488:
7465:
7390:
7376:
6215:
6206:
6100:
6091:
3490:, which is thus invariant on the set of all
1612:
1578:
1464:
1430:
562:
528:
476:
442:
369:
335:
9145:Note that the probability mass function of
8184:need for specialized modifications such as
7413:{\displaystyle \{x_{\ell }\}_{\ell =1}^{M}}
6188:), a similar asymptotic normality applies:
4767:of order statistics may be sampled from an
2934:which is (up to terms of higher order than
10422:
10384:
10370:
6641:being independent identically distributed
1866:we obtain the corresponding random sample
16:Kth smallest value in a statistical sample
11035:
10258:
10209:
10192:"On Some Useful "Inefficient" Statistics"
10186:
10144:
10078:from the uniform distribution (on (0,1)).
9936:Learn how and when to remove this message
9825:â linear combinations of order statistics
8248:{\displaystyle X_{1},X_{2},\ldots ,X_{n}}
8041:10: Compute the density estimate at
7199:
4946:
4843:
2953:
1772:{\displaystyle X_{1},X_{2},\ldots ,X_{n}}
1611:
1581:
1463:
1433:
791:
561:
531:
475:
445:
368:
338:
256:
10180:
10020:
10018:
9899:This article includes a list of general
7750:observations each. 4: Create a vector
7619:{\displaystyle s_{N}={\frac {N}{m_{N}}}}
115:
18:
9995:Casella, George; Berger, Roger (2002).
1720:We assume throughout this section that
887:independent and identically distributed
12690:
12348:KaplanâMeier estimator (product limit)
10024:
9962:David, H. A.; Nagaraja, H. N. (2003).
7779:to hold the density evaluations. 5:
7342:. This equation in combination with a
6180:with a continuous non-zero density at
4853:{\displaystyle dF_{X}(x)=f_{X}(x)\,dx}
2993:sample elements fall in the intervals
1977:{\displaystyle U_{(i)}=F_{X}(X_{(i)})}
280:enclosed in parentheses indicates the
128:the order statistics would be denoted
12421:
11988:
11735:
11034:
10804:
10421:
10365:
10336:
10121:
10051:
10015:
9769:can be used and the time taken is O(
8681: observations greater than
7862:7: Find the nearest distance
6408:, while the mean performs better for
6056:
3926:The formula follows from noting that
12658:
12358:Accelerated failure time (AFT) model
10162:Statistics & Probability Letters
9955:
9885:
6645:random variables with rate 1. Since
4573:{\displaystyle X_{1},X_{2},..,X_{n}}
2490:respectively. This equals (refer to
12670:
11953:Analysis of variance (ANOVA, anova)
10805:
10127:"On the theory of order statistics"
8316:. To find the probabilities of the
6783:{\displaystyle Y_{i}=|X_{i}-x^{*}|}
4860:, and we can use the substitutions
2376:observations fall in the intervals
2313:, and that at least one is between
1905:{\displaystyle U_{1},\ldots ,U_{n}}
13:
12048:CochranâMantelâHaenszel statistics
10674:Pearson product-moment correlation
9905:it lacks sufficient corresponding
9539:
9342:
9045:
8945: observations less than
8737:
6473:
6069:sample quantile is asymptotically
6033:
5970:
5945:
5920:
5874:
5816:
3625:{\displaystyle n\geq k>j\geq 1}
2661:joint probability density function
1859:{\displaystyle U_{i}=F_{X}(X_{i})}
1057:
984:specifies which order statistic):
523:
520:
517:
514:
511:
288:th order statistic of the sample.
14:
12719:
10319:
10197:Annals of Mathematical Statistics
7659:{\displaystyle s_{N}\times m_{N}}
6383:relative entropy or KL divergence
6061:For the uniform distribution, as
3196:order statistics turns out to be
2635:The mean of this distribution is
716:and there are two middle values,
619:A similar important statistic in
58:th-smallest value. Together with
12669:
12657:
12645:
12632:
12631:
12422:
10241:Garg, Vikram V.; Tenorio, Luis;
9890:
6727:. Consider the random variables
5787:of the underlying distribution.
2234:
388:Similarly, for a sample of size
106:cumulative distribution function
12307:Least-squares spectral analysis
10283:
10234:
8870:{\displaystyle P(X_{(k)}<x)}
8192:Dealing with discrete variables
6568:
6412:that are normally distributed.
4970:drawn from the distribution of
4956:{\displaystyle du=f_{X}(x)\,dx}
3677:{\displaystyle U_{(k)}-U_{(j)}}
3587:{\displaystyle U_{(n)}-U_{(1)}}
2305:, it is necessary that exactly
96:to analyze order statistics of
11288:Mean-unbiased minimum-variance
10391:
10225:
10153:
10115:
10083:
10045:
9988:
9701:
9697:
9691:
9682:
9676:
9670:
9661:
9657:
9651:
9642:
9636:
9624:
9606:
9602:
9596:
9590:
9581:
9577:
9571:
9559:
9472:
9458:
9449:
9422:
9404:
9377:
9292:
9281:
9275:
9267:
9258:
9247:
9241:
9233:
9220:
9209:
9203:
9195:
9163:
9157:
9110:
9096:
9087:
9060:
8995:
8970:
8951:
8932:
8919:
8908:
8902:
8894:
8864:
8853:
8847:
8839:
8794:
8767:
8687:
8662:
8643:
8624:
8611:
8600:
8594:
8586:
8523:
8517:
8502:
8490:
8463:
8457:
8448:
8436:
8411:
8405:
8396:
8390:
8381:
8369:
8303:
8297:
8271:
8265:
8157:
8111:
8092:
8068:
7836:
7798:
7763:
7566:
7547:
7475:
7445:
7433:
7323:
7310:
7307:
7295:
7289:
7283:
7196:
7190:
7171:
7165:
7136:
7124:
7121:
7109:
7094:
7088:
7082:
7070:
7058:
7053:
7047:
7039:
6991:
6985:
6951:
6945:
6926:
6913:
6883:
6864:
6848:
6829:
6813:
6807:
6776:
6748:
6457:
6433:
6323:
6319:
6316:
6310:
6294:
6288:
6280:
6268:
6256:
6250:
6218:
6203:
6146:
6134:
6103:
6088:
6073:, since it is approximated by
6005:
5990:
5846:
5831:
5700:
5687:
5671:
5658:
5636:
5604:
5597:
5591:
5572:
5566:
5507:
5501:
5488:
5482:
5457:
5453:
5447:
5428:
5407:
5403:
5397:
5381:
5375:
5362:
5347:
5343:
5337:
5324:
5315:
5303:
5297:
5279:
5273:
5261:
5244:
5232:
5225:
5219:
5206:
5200:
5167:
5161:
5136:
5132:
5126:
5107:
5092:
5088:
5082:
5069:
5060:
5048:
5042:
5030:
5013:
5007:
5000:
4994:
4943:
4937:
4892:
4886:
4840:
4834:
4818:
4812:
4634:
4628:
4497:
4488:
4476:
4455:
4420:
4408:
4399:
4386:
4381:
4372:
4360:
4351:
4348:
4336:
4327:
4321:
4295:
4290:
4284:
4271:
4265:
4257:
4236:
4224:
4215:
4202:
4197:
4179:
4164:
4152:
4143:
4130:
4125:
4107:
4095:
4090:
4084:
4071:
4065:
4057:
4039:
4034:
4028:
4020:
4008:
4003:
3997:
3989:
3977:
3972:
3966:
3953:
3947:
3939:
3910:
3898:
3889:
3876:
3871:
3853:
3841:
3836:
3830:
3817:
3811:
3803:
3777:
3768:
3756:
3735:
3721:
3715:
3702:
3696:
3684:also has a beta distribution:
3669:
3663:
3650:
3644:
3579:
3573:
3560:
3554:
3358:! is the volume of the region
3322:
3277:
3270:
3264:
3245:
3239:
3226:
3220:
3176:
3155:
3135:
3114:
3094:
3073:
3053:
3032:
3012:
3000:
2960:
2944:
2912:
2900:
2883:
2870:
2858:
2840:
2817:
2804:
2792:
2780:
2749:
2737:
2730:
2724:
2711:
2705:
2604:
2582:
2545:
2533:
2527:
2515:
2477:
2456:
2436:
2415:
2395:
2383:
2351:
2335:
2278:
2272:
2241:
2215:
2201:
2195:
2144:
2131:
2106:
2094:
2088:
2076:
2059:
2053:
2046:
2040:
2005:
1999:
1971:
1966:
1960:
1952:
1934:
1928:
1853:
1840:
1662:
1658:
1652:
1633:
1621:
1572:
1560:
1554:
1547:
1541:
1502:
1498:
1492:
1479:
1473:
1424:
1412:
1406:
1399:
1393:
1342:
1338:
1332:
1313:
1298:
1294:
1288:
1275:
1272:
1266:
1247:
1235:
1229:
1217:
1200:
1194:
1187:
1181:
1133:
1129:
1123:
1104:
1095:
1091:
1085:
1072:
1023:
1017:
1010:
1004:
967:
961:
911:joint probability distribution
773:
761:
734:
728:
681:
669:
598:
592:
579:
573:
431:
425:
324:
318:
242:
236:
211:
205:
180:
174:
149:
143:
1:
12601:Geographic information system
11817:Simultaneous equations models
9948:
9756:The problem of computing the
8562:{\displaystyle k^{\text{th}}}
8336:{\displaystyle k^{\text{th}}}
4792:, it has a density such that
4771:via a path counting method .
3483:{\displaystyle {\sqrt {2sn}}}
3453:{\displaystyle 0<s<n/2}
24:Probability density functions
11784:Coefficient of determination
11395:Uniformly most powerful test
10269:10.1080/03610926.2014.988260
10066:10.1016/j.stamet.2008.04.001
9840:Examples of order statistics
7852:{\displaystyle k=1\to m_{N}}
7807:{\displaystyle \ell =1\to M}
2663:of the two order statistics
936:) are discussed at the end.
926:probability density function
657:, then the sample median is
7:
12353:Proportional hazards models
12297:Spectral density estimation
12279:Vector autoregression (VAR)
11713:Maximum posterior estimator
10945:Randomized controlled trial
9807:FisherâTippett distribution
9780:
7026:total observations yields,
6176:For a general distribution
5791:A small-sample-size example
2981: â 1 â
796:Given any random variables
10:
12724:
12113:Multivariate distributions
10533:Average absolute deviation
10132:Acta Mathematica Hungarica
9881:Sample mean and covariance
9846:Sample maximum and minimum
9745:
9742:Computing order statistics
8166:{\displaystyle {\hat {f}}}
7885:{\displaystyle d_{\ell k}}
7772:{\displaystyle {\hat {f}}}
7451:{\displaystyle a\in (0,1)}
4898:{\displaystyle u=F_{X}(x)}
858:When the random variables
12627:
12581:
12518:
12471:
12434:
12430:
12417:
12389:
12371:
12338:
12329:
12287:
12234:
12195:
12144:
12135:
12101:Structural equation model
12056:
12013:
12009:
11984:
11943:
11909:
11863:
11830:
11792:
11759:
11755:
11731:
11671:
11580:
11499:
11463:
11454:
11437:Score/Lagrange multiplier
11422:
11375:
11320:
11246:
11237:
11047:
11043:
11030:
10989:
10963:
10915:
10870:
10852:Sample size determination
10817:
10813:
10800:
10704:
10659:
10633:
10615:
10571:
10523:
10443:
10434:
10430:
10417:
10399:
10174:10.1016/j.spl.2009.09.006
10025:Gentle, James E. (2009),
8286:probability mass function
7912:{\displaystyle x_{\ell }}
7458:(usually 1/3). Output:
2966:{\displaystyle O(du\,dv)}
2357:{\displaystyle O(du^{2})}
928:(PDF), that is, they are
781:{\displaystyle X_{(m+1)}}
689:{\displaystyle X_{(m+1)}}
621:exploratory data analysis
64:non-parametric statistics
34:with unit scale parameter
12698:Nonparametric statistics
12596:Environmental statistics
12118:Elliptical distributions
11911:Generalized linear model
11840:Simple linear regression
11610:HodgesâLehmann estimator
11067:Probability distribution
10976:Stochastic approximation
10538:Coefficient of variation
10357:Dynamic Order Statistics
10332:. Retrieved Feb 02, 2005
10031:, Springer, p. 63,
10028:Computational Statistics
9802:Concomitant (statistics)
8937:there are at least
8629:there are at least
6415:
4586:exponential distribution
4580:a random sample of size
4308:and comparing that with
3182:{\displaystyle (v+dv,1)}
3141:{\displaystyle (v,v+dv)}
3100:{\displaystyle (u+du,v)}
3059:{\displaystyle (u,u+du)}
2632:and the result follows.
2492:multinomial distribution
2483:{\displaystyle (u+du,1)}
2442:{\displaystyle (u,u+du)}
973:{\displaystyle F_{X}(x)}
819:, the order statistics X
303:of the sample, that is,
297:smallest order statistic
32:exponential distribution
12256:Cross-correlation (XCF)
11864:Non-standard predictors
11298:LehmannâScheffĂ© theorem
10971:Adaptive clinical trial
10211:10.1214/aoms/1177730881
10054:Statistical Methodology
9920:more precise citations.
9171:{\displaystyle X_{(k)}}
8975:there are at most
8667:there are at most
6999:{\displaystyle Y_{(1)}}
6065:tends to infinity, the
5539:{\displaystyle x\leq y}
4611:each have distribution
4592:, the order statistics
2973:) the probability that
2286:{\displaystyle U_{(k)}}
2013:{\displaystyle U_{(k)}}
742:{\displaystyle X_{(m)}}
404:largest order statistic
402:th order statistic (or
102:continuous distribution
30: = 5 from an
12652:Mathematics portal
12473:Engineering statistics
12381:NelsonâAalen estimator
11958:Analysis of covariance
11845:Ordinary least squares
11769:Pearson product-moment
11173:Statistical functional
11084:Empirical distribution
10917:Controlled experiments
10646:Frequency distribution
10424:Descriptive statistics
10352:Retrieved Feb 02, 2005
10300:10.1002/0471722162.ch3
10100:10.1002/0471722162.ch2
9829:Rank-size distribution
9732:
9531:
9334:
9172:
9136:
9037:
8871:
8820:
8729:
8563:
8533:
8337:
8310:
8278:
8249:
8167:
8131:
8035:
8003:
7933:
7913:
7886:
7853:
7808:
7773:
7744:
7717:
7690:
7689:{\displaystyle M_{ij}}
7660:
7620:
7573:
7512:
7452:
7414:
7363:
7336:
7260:
7233:
7210:
7020:
7000:
6964:
6890:
6784:
6721:
6694:
6625:
6607:
6554:
6509:
6344:
6167:
6043:
5884:
5769:
5707:
5540:
5514:
5174:
4957:
4899:
4854:
4731:
4690:
4574:
4504:
4430:
4302:
3920:
3784:
3678:
3626:
3588:
3533:
3516:with constant product
3510:
3484:
3454:
3410:
3341:
3183:
3142:
3101:
3060:
3019:
2967:
2925:
2623:
2484:
2443:
2402:
2368: â 1, 1 and
2358:
2287:
2251:
2163:
2014:
1978:
1906:
1860:
1804:
1773:
1707:marginal distributions
1675:
1515:
1364:
1152:
1049:
974:
934:discrete distributions
792:Probabilistic analysis
782:
743:
690:
640:. More precisely, if
610:
486:
376:
261:
35:
12568:Population statistics
12510:System identification
12244:Autocorrelation (ACF)
12172:Exponential smoothing
12086:Discriminant analysis
12081:Canonical correlation
11945:Partition of variance
11807:Regression validation
11651:(JonckheereâTerpstra)
11550:Likelihood-ratio test
11239:Frequentist inference
11151:Locationâscale family
11072:Sampling distribution
11037:Statistical inference
11004:Cross-sectional study
10991:Observational studies
10950:Randomized experiment
10779:Stem-and-leaf display
10581:Central limit theorem
9998:Statistical Inference
9733:
9505:
9308:
9173:
9137:
9011:
8872:
8821:
8703:
8564:
8534:
8338:
8311:
8279:
8250:
8168:
8132:
8036:
7976:
7934:
7914:
7892:to the current point
7887:
7854:
7809:
7774:
7745:
7743:{\displaystyle s_{N}}
7718:
7716:{\displaystyle m_{N}}
7691:
7661:
7621:
7574:
7513:
7453:
7415:
7364:
7337:
7261:
7259:{\displaystyle g_{Y}}
7234:
7211:
7021:
7001:
6965:
6891:
6785:
6722:
6720:{\displaystyle x^{*}}
6695:
6693:{\displaystyle f_{X}}
6626:
6575:
6534:
6510:
6420:It can be shown that
6394:central limit theorem
6345:
6168:
6044:
5885:
5770:
5708:
5541:
5515:
5175:
4958:
4900:
4855:
4790:absolutely continuous
4732:
4670:
4575:
4505:
4431:
4303:
3921:
3785:
3679:
3627:
3589:
3534:
3511:
3485:
3455:
3411:
3342:
3184:
3143:
3102:
3061:
3020:
3018:{\displaystyle (0,u)}
2968:
2926:
2624:
2485:
2444:
2403:
2401:{\displaystyle (0,u)}
2359:
2288:
2252:
2164:
2015:
1979:
1907:
1861:
1805:
1803:{\displaystyle F_{X}}
1774:
1676:
1516:
1365:
1153:
1029:
975:
930:absolutely continuous
855:in increasing order.
783:
744:
691:
611:
487:
377:
293:first order statistic
262:
116:Notation and examples
22:
12491:Probabilistic design
12076:Principal components
11919:Exponential families
11871:Nonlinear regression
11850:General linear model
11812:Mixed effects models
11802:Errors and residuals
11779:Confounding variable
11681:Bayesian probability
11659:Van der Waerden test
11649:Ordered alternative
11414:Multiple comparisons
11293:RaoâBlackwellization
11256:Estimating equations
11212:Statistical distance
10930:Factorial experiment
10463:Arithmetic-Geometric
10188:Mosteller, Frederick
9818:Bernstein polynomial
9185:
9149:
8884:
8833:
8576:
8546:
8350:
8320:
8309:{\displaystyle f(x)}
8291:
8277:{\displaystyle F(x)}
8259:
8200:
8186:IQR based bandwidths
8148:
8045:
7947:
7939:th subset 8:
7923:
7896:
7866:
7824:
7786:
7754:
7727:
7700:
7670:
7630:
7583:
7525:
7462:
7424:
7373:
7353:
7270:
7243:
7223:
7033:
7010:
6977:
6900:
6794:
6731:
6704:
6677:
6525:
6427:
6406:Laplace distribution
6195:
6080:
6071:normally distributed
5905:
5806:
5717:
5553:
5524:
5187:
4981:
4915:
4867:
4796:
4620:
4522:
4440:
4312:
3930:
3794:
3688:
3636:
3598:
3546:
3520:
3494:
3464:
3460:is bounded above by
3424:
3362:
3207:
3152:
3111:
3070:
3029:
2997:
2938:
2692:
2501:
2453:
2412:
2380:
2329:
2264:
2187:
2027:
1991:
1920:
1914:uniform distribution
1870:
1814:
1787:
1724:
1699:uniform distribution
1528:
1380:
1168:
991:
948:
753:
720:
661:
506:
417:
310:
270:where the subscript
135:
110:uniform distribution
12563:Official statistics
12486:Methods engineering
12167:Seasonal adjustment
11935:Poisson regressions
11855:Bayesian regression
11794:Regression analysis
11774:Partial correlation
11746:Regression analysis
11345:Prediction interval
11340:Likelihood interval
11330:Confidence interval
11322:Interval estimation
11283:Unbiased estimators
11101:Model specification
10981:Up-and-down designs
10669:Partial correlation
10625:Index of dispersion
10543:Interquartile range
9834:Selection algorithm
9748:Selection algorithm
9376:
8766:
7507:
7409:
7349:Input: A sample of
7156:
6375:Frederick Mosteller
4769:Erlang distribution
3509:{\displaystyle s,n}
2977: â 1, 1,
2685:can be shown to be
636:of observations is
625:interquartile range
12703:Summary statistics
12583:Spatial statistics
12463:Medical statistics
12363:First hitting time
12317:Whittle likelihood
11968:Degrees of freedom
11963:Multivariate ANOVA
11896:Heteroscedasticity
11708:Bayesian estimator
11673:Bayesian inference
11522:KolmogorovâSmirnov
11407:Randomization test
11377:Testing hypotheses
11350:Tolerance interval
11261:Maximum likelihood
11156:Exponential family
11089:Density estimation
11049:Statistical theory
11009:Natural experiment
10955:Scientific control
10872:Survey methodology
10558:Standard deviation
10338:Weisstein, Eric W.
10146:10.1007/BF02127580
9972:10.1002/0471722162
9728:
9726:
9362:
9168:
9132:
9130:
8867:
8816:
8814:
8752:
8559:
8529:
8333:
8306:
8274:
8245:
8163:
8127:
8031:
7929:
7909:
7882:
7849:
7804:
7769:
7740:
7713:
7686:
7656:
7616:
7569:
7508:
7487:
7448:
7410:
7389:
7359:
7332:
7256:
7229:
7206:
7142:
7016:
7006:given a sample of
6996:
6960:
6886:
6780:
6717:
6690:
6621:
6505:
6340:
6163:
6057:Large sample sizes
6039:
5880:
5765:
5703:
5536:
5510:
5170:
4953:
4895:
4850:
4727:
4570:
4500:
4426:
4298:
3916:
3780:
3674:
3622:
3584:
3532:{\displaystyle sn}
3529:
3506:
3480:
3450:
3406:
3337:
3179:
3138:
3097:
3056:
3015:
2963:
2921:
2619:
2480:
2439:
2398:
2354:
2283:
2247:
2159:
2010:
1974:
1912:from the standard
1902:
1856:
1800:
1769:
1671:
1511:
1360:
1148:
970:
778:
739:
686:
606:
482:
372:
257:
94:probability theory
52:statistical sample
36:
12685:
12684:
12623:
12622:
12619:
12618:
12558:National accounts
12528:Actuarial science
12520:Social statistics
12413:
12412:
12409:
12408:
12405:
12404:
12340:Survival function
12325:
12324:
12187:Granger causality
12028:Contingency table
12003:Survival analysis
11980:
11979:
11976:
11975:
11832:Linear regression
11727:
11726:
11723:
11722:
11698:Credible interval
11667:
11666:
11450:
11449:
11266:Method of moments
11135:Parametric family
11096:Statistical model
11026:
11025:
11022:
11021:
10940:Random assignment
10862:Statistical power
10796:
10795:
10792:
10791:
10641:Contingency table
10611:
10610:
10478:Generalized/power
10341:"Order Statistic"
9946:
9945:
9938:
9812:BapatâBeg theorem
9767:sorting algorithm
9752:Sampling in order
9546:
9349:
9052:
8990:
8976:
8946:
8938:
8744:
8682:
8668:
8638:
8630:
8556:
8472:
8419:
8330:
8160:
8125:
8071:
8029:
7932:{\displaystyle k}
7766:
7614:
7478:
7362:{\displaystyle N}
7232:{\displaystyle Q}
7140:
7098:
7019:{\displaystyle N}
6958:
6896:. In particular,
6500:
6483:
6478:
6462:
6367:quantile function
6333:
6153:
6025:
5977:
5952:
5927:
5866:
5823:
5322:
5067:
4765:Laplace transform
4720:
4663:
4652:
4424:
4240:
4168:
3914:
3478:
2919:
2865:
2799:
2552:
2180:random variable.
2113:
1711:beta distribution
1709:belonging to the
1254:
1064:
915:BapatâBeg theorem
651:for some integer
230:
227:
199:
196:
168:
165:
12715:
12673:
12672:
12661:
12660:
12650:
12649:
12635:
12634:
12538:Crime statistics
12432:
12431:
12419:
12418:
12336:
12335:
12302:Fourier analysis
12289:Frequency domain
12269:
12216:
12182:Structural break
12142:
12141:
12091:Cluster analysis
12038:Log-linear model
12011:
12010:
11986:
11985:
11927:
11901:Homoscedasticity
11757:
11756:
11733:
11732:
11652:
11644:
11636:
11635:(KruskalâWallis)
11620:
11605:
11560:Cross validation
11545:
11527:AndersonâDarling
11474:
11461:
11460:
11432:Likelihood-ratio
11424:Parametric tests
11402:Permutation test
11385:1- & 2-tails
11276:Minimum distance
11248:Point estimation
11244:
11243:
11195:Optimal decision
11146:
11045:
11044:
11032:
11031:
11014:Quasi-experiment
10964:Adaptive designs
10815:
10814:
10802:
10801:
10679:Rank correlation
10441:
10440:
10432:
10431:
10419:
10418:
10386:
10379:
10372:
10363:
10362:
10351:
10350:
10326:Order statistics
10313:
10312:
10292:Order Statistics
10287:
10281:
10280:
10262:
10238:
10232:
10229:
10223:
10222:
10220:
10218:
10213:
10184:
10178:
10177:
10157:
10151:
10150:
10148:
10119:
10113:
10112:
10092:Order Statistics
10087:
10081:
10080:
10049:
10043:
10041:
10022:
10013:
10012:
9992:
9986:
9985:
9964:Order Statistics
9959:
9941:
9934:
9930:
9927:
9921:
9916:this article by
9907:inline citations
9894:
9893:
9886:
9737:
9735:
9734:
9729:
9727:
9720:
9716:
9715:
9714:
9669:
9668:
9620:
9619:
9589:
9588:
9553:
9552:
9551:
9538:
9530:
9519:
9498:
9491:
9487:
9486:
9485:
9470:
9469:
9457:
9456:
9447:
9446:
9434:
9433:
9418:
9417:
9402:
9401:
9389:
9388:
9375:
9370:
9356:
9355:
9354:
9341:
9333:
9322:
9301:
9285:
9284:
9251:
9250:
9213:
9212:
9177:
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9174:
9169:
9167:
9166:
9141:
9139:
9138:
9133:
9131:
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9123:
9108:
9107:
9095:
9094:
9085:
9084:
9072:
9071:
9059:
9058:
9057:
9044:
9036:
9025:
9004:
8991:
8988:
8977:
8974:
8960:
8947:
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8912:
8911:
8876:
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8857:
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8817:
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8792:
8791:
8779:
8778:
8765:
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8751:
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8749:
8736:
8728:
8717:
8696:
8683:
8680:
8669:
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8652:
8639:
8636:
8631:
8628:
8604:
8603:
8568:
8566:
8565:
8560:
8558:
8557:
8554:
8538:
8536:
8535:
8530:
8483:
8482:
8473:
8470:
8429:
8428:
8417:
8362:
8361:
8342:
8340:
8339:
8334:
8332:
8331:
8328:
8315:
8313:
8312:
8307:
8283:
8281:
8280:
8275:
8254:
8252:
8251:
8246:
8244:
8243:
8225:
8224:
8212:
8211:
8172:
8170:
8169:
8164:
8162:
8161:
8153:
8136:
8134:
8133:
8128:
8126:
8124:
8123:
8122:
8110:
8109:
8084:
8079:
8078:
8073:
8072:
8064:
8057:
8056:
8040:
8038:
8037:
8032:
8030:
8028:
8027:
8018:
8017:
8005:
8002:
8001:
8000:
7990:
7972:
7971:
7959:
7958:
7938:
7936:
7935:
7930:
7918:
7916:
7915:
7910:
7908:
7907:
7891:
7889:
7888:
7883:
7881:
7880:
7858:
7856:
7855:
7850:
7848:
7847:
7813:
7811:
7810:
7805:
7778:
7776:
7775:
7770:
7768:
7767:
7759:
7749:
7747:
7746:
7741:
7739:
7738:
7722:
7720:
7719:
7714:
7712:
7711:
7695:
7693:
7692:
7687:
7685:
7684:
7665:
7663:
7662:
7657:
7655:
7654:
7642:
7641:
7625:
7623:
7622:
7617:
7615:
7613:
7612:
7600:
7595:
7594:
7578:
7576:
7575:
7570:
7565:
7564:
7537:
7536:
7517:
7515:
7514:
7509:
7506:
7501:
7486:
7485:
7480:
7479:
7471:
7457:
7455:
7454:
7449:
7419:
7417:
7416:
7411:
7408:
7403:
7388:
7387:
7368:
7366:
7365:
7360:
7341:
7339:
7338:
7333:
7331:
7330:
7282:
7281:
7265:
7263:
7262:
7257:
7255:
7254:
7238:
7236:
7235:
7230:
7215:
7213:
7212:
7207:
7189:
7188:
7164:
7155:
7150:
7141:
7139:
7104:
7099:
7097:
7065:
7057:
7056:
7025:
7023:
7022:
7017:
7005:
7003:
7002:
6997:
6995:
6994:
6969:
6967:
6966:
6961:
6959:
6954:
6944:
6943:
6933:
6925:
6924:
6912:
6911:
6895:
6893:
6892:
6887:
6876:
6875:
6863:
6862:
6847:
6846:
6828:
6827:
6806:
6805:
6789:
6787:
6786:
6781:
6779:
6774:
6773:
6761:
6760:
6751:
6743:
6742:
6726:
6724:
6723:
6718:
6716:
6715:
6699:
6697:
6696:
6691:
6689:
6688:
6630:
6628:
6627:
6622:
6617:
6616:
6606:
6595:
6564:
6563:
6553:
6548:
6514:
6512:
6511:
6506:
6501:
6499:
6485:
6481:
6480:
6479:
6477:
6476:
6470:
6465:
6460:
6369:associated with
6359:density function
6349:
6347:
6346:
6341:
6339:
6335:
6334:
6332:
6331:
6330:
6309:
6308:
6283:
6263:
6249:
6248:
6222:
6221:
6172:
6170:
6169:
6164:
6159:
6155:
6154:
6149:
6129:
6107:
6106:
6048:
6046:
6045:
6040:
6026:
6018:
6013:
6012:
6000:
5989:
5985:
5984:
5983:
5982:
5969:
5959:
5958:
5957:
5944:
5934:
5933:
5932:
5919:
5889:
5887:
5886:
5881:
5867:
5859:
5854:
5853:
5841:
5830:
5829:
5828:
5815:
5774:
5772:
5771:
5766:
5761:
5760:
5742:
5741:
5729:
5728:
5712:
5710:
5709:
5704:
5699:
5698:
5686:
5685:
5670:
5669:
5657:
5656:
5635:
5634:
5616:
5615:
5603:
5602:
5601:
5600:
5576:
5575:
5545:
5543:
5542:
5537:
5519:
5517:
5516:
5511:
5500:
5499:
5481:
5480:
5471:
5470:
5446:
5445:
5427:
5426:
5396:
5395:
5374:
5373:
5361:
5360:
5336:
5335:
5323:
5321:
5259:
5251:
5231:
5230:
5229:
5228:
5210:
5209:
5179:
5177:
5176:
5171:
5160:
5159:
5150:
5149:
5125:
5124:
5106:
5105:
5081:
5080:
5068:
5066:
5028:
5020:
5006:
5005:
5004:
5003:
4962:
4960:
4959:
4954:
4936:
4935:
4904:
4902:
4901:
4896:
4885:
4884:
4859:
4857:
4856:
4851:
4833:
4832:
4811:
4810:
4736:
4734:
4733:
4728:
4726:
4722:
4721:
4719:
4702:
4701:
4692:
4689:
4684:
4664:
4656:
4654:
4653:
4651:
4646:
4641:
4638:
4637:
4579:
4577:
4576:
4571:
4569:
4568:
4547:
4546:
4534:
4533:
4509:
4507:
4506:
4501:
4435:
4433:
4432:
4427:
4425:
4423:
4407:
4406:
4384:
4334:
4307:
4305:
4304:
4299:
4294:
4293:
4275:
4274:
4241:
4239:
4223:
4222:
4200:
4174:
4169:
4167:
4151:
4150:
4128:
4102:
4094:
4093:
4075:
4074:
4038:
4037:
4007:
4006:
3976:
3975:
3957:
3956:
3925:
3923:
3922:
3917:
3915:
3913:
3897:
3896:
3874:
3848:
3840:
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3821:
3820:
3789:
3787:
3786:
3781:
3725:
3724:
3706:
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3623:
3593:
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3564:
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3538:
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3513:
3512:
3507:
3489:
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3468:
3459:
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3415:
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3407:
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3321:
3320:
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3289:
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2800:
2798:
2778:
2777:
2762:
2736:
2735:
2734:
2733:
2715:
2714:
2674: <
2655: <
2628:
2626:
2625:
2620:
2618:
2617:
2569:
2568:
2553:
2551:
2513:
2505:
2489:
2487:
2486:
2481:
2448:
2446:
2445:
2440:
2407:
2405:
2404:
2399:
2363:
2361:
2360:
2355:
2350:
2349:
2292:
2290:
2289:
2284:
2282:
2281:
2256:
2254:
2253:
2248:
2237:
2205:
2204:
2178:beta-distributed
2168:
2166:
2165:
2160:
2158:
2157:
2130:
2129:
2114:
2112:
2074:
2066:
2052:
2051:
2050:
2049:
2019:
2017:
2016:
2011:
2009:
2008:
1983:
1981:
1980:
1975:
1970:
1969:
1951:
1950:
1938:
1937:
1911:
1909:
1908:
1903:
1901:
1900:
1882:
1881:
1865:
1863:
1862:
1857:
1852:
1851:
1839:
1838:
1826:
1825:
1809:
1807:
1806:
1801:
1799:
1798:
1778:
1776:
1775:
1770:
1768:
1767:
1749:
1748:
1736:
1735:
1680:
1678:
1677:
1672:
1670:
1669:
1651:
1650:
1610:
1609:
1591:
1590:
1553:
1552:
1551:
1550:
1520:
1518:
1517:
1512:
1510:
1509:
1491:
1490:
1462:
1461:
1443:
1442:
1405:
1404:
1403:
1402:
1369:
1367:
1366:
1361:
1356:
1355:
1331:
1330:
1312:
1311:
1287:
1286:
1265:
1264:
1255:
1253:
1215:
1207:
1193:
1192:
1191:
1190:
1157:
1155:
1154:
1149:
1147:
1146:
1122:
1121:
1103:
1102:
1084:
1083:
1071:
1070:
1069:
1056:
1048:
1043:
1016:
1015:
1014:
1013:
979:
977:
976:
971:
960:
959:
913:is given by the
787:
785:
784:
779:
777:
776:
748:
746:
745:
740:
738:
737:
715:
701:
695:
693:
692:
687:
685:
684:
656:
650:
635:
615:
613:
612:
607:
602:
601:
583:
582:
560:
559:
541:
540:
527:
526:
491:
489:
488:
483:
474:
473:
455:
454:
435:
434:
401:
400:
393:
381:
379:
378:
373:
367:
366:
348:
347:
328:
327:
299:) is always the
287:
286:
279:
277:
266:
264:
263:
258:
246:
245:
228:
225:
215:
214:
197:
194:
184:
183:
166:
163:
153:
152:
87:sample quantiles
54:is equal to its
12723:
12722:
12718:
12717:
12716:
12714:
12713:
12712:
12688:
12687:
12686:
12681:
12644:
12615:
12577:
12514:
12500:quality control
12467:
12449:Clinical trials
12426:
12401:
12385:
12373:Hazard function
12367:
12321:
12283:
12267:
12230:
12226:BreuschâGodfrey
12214:
12191:
12131:
12106:Factor analysis
12052:
12033:Graphical model
12005:
11972:
11939:
11925:
11905:
11859:
11826:
11788:
11751:
11750:
11719:
11663:
11650:
11642:
11634:
11618:
11603:
11582:Rank statistics
11576:
11555:Model selection
11543:
11501:Goodness of fit
11495:
11472:
11446:
11418:
11371:
11316:
11305:Median unbiased
11233:
11144:
11077:Order statistic
11039:
11018:
10985:
10959:
10911:
10866:
10809:
10807:Data collection
10788:
10700:
10655:
10629:
10607:
10567:
10519:
10436:Continuous data
10426:
10413:
10395:
10390:
10322:
10317:
10316:
10310:
10288:
10284:
10239:
10235:
10230:
10226:
10216:
10214:
10185:
10181:
10158:
10154:
10120:
10116:
10110:
10088:
10084:
10050:
10046:
10039:
10023:
10016:
10009:
9993:
9989:
9982:
9960:
9956:
9951:
9942:
9931:
9925:
9922:
9912:Please help to
9911:
9895:
9891:
9842:
9783:
9754:
9746:Main articles:
9744:
9725:
9724:
9704:
9700:
9664:
9660:
9609:
9605:
9584:
9580:
9558:
9554:
9547:
9534:
9533:
9532:
9520:
9509:
9496:
9495:
9475:
9471:
9465:
9461:
9452:
9448:
9442:
9438:
9429:
9425:
9407:
9403:
9397:
9393:
9384:
9380:
9371:
9366:
9361:
9357:
9350:
9337:
9336:
9335:
9323:
9312:
9299:
9298:
9274:
9270:
9240:
9236:
9223:
9202:
9198:
9188:
9186:
9183:
9182:
9156:
9152:
9150:
9147:
9146:
9129:
9128:
9113:
9109:
9103:
9099:
9090:
9086:
9080:
9076:
9067:
9063:
9053:
9040:
9039:
9038:
9026:
9015:
9002:
9001:
8987:
8973:
8958:
8957:
8943:
8935:
8922:
8901:
8897:
8887:
8885:
8882:
8881:
8846:
8842:
8834:
8831:
8830:
8813:
8812:
8797:
8793:
8787:
8783:
8774:
8770:
8761:
8756:
8745:
8732:
8731:
8730:
8718:
8707:
8694:
8693:
8679:
8665:
8650:
8649:
8635:
8627:
8614:
8593:
8589:
8579:
8577:
8574:
8573:
8553:
8549:
8547:
8544:
8543:
8478:
8474:
8471: and
8469:
8424:
8420:
8357:
8353:
8351:
8348:
8347:
8327:
8323:
8321:
8318:
8317:
8292:
8289:
8288:
8260:
8257:
8256:
8239:
8235:
8220:
8216:
8207:
8203:
8201:
8198:
8197:
8194:
8173:
8152:
8151:
8149:
8146:
8145:
8118:
8114:
8105:
8101:
8088:
8083:
8074:
8063:
8062:
8061:
8052:
8048:
8046:
8043:
8042:
8023:
8019:
8010:
8006:
8004:
7996:
7992:
7991:
7980:
7967:
7963:
7954:
7950:
7948:
7945:
7944:
7924:
7921:
7920:
7903:
7899:
7897:
7894:
7893:
7873:
7869:
7867:
7864:
7863:
7843:
7839:
7825:
7822:
7821:
7787:
7784:
7783:
7758:
7757:
7755:
7752:
7751:
7734:
7730:
7728:
7725:
7724:
7707:
7703:
7701:
7698:
7697:
7677:
7673:
7671:
7668:
7667:
7650:
7646:
7637:
7633:
7631:
7628:
7627:
7608:
7604:
7599:
7590:
7586:
7584:
7581:
7580:
7554:
7550:
7532:
7528:
7526:
7523:
7522:
7519:
7502:
7491:
7481:
7470:
7469:
7468:
7463:
7460:
7459:
7425:
7422:
7421:
7404:
7393:
7383:
7379:
7374:
7371:
7370:
7354:
7351:
7350:
7326:
7322:
7277:
7273:
7271:
7268:
7267:
7250:
7246:
7244:
7241:
7240:
7224:
7221:
7220:
7178:
7174:
7157:
7151:
7146:
7108:
7103:
7069:
7064:
7046:
7042:
7034:
7031:
7030:
7011:
7008:
7007:
6984:
6980:
6978:
6975:
6974:
6939:
6935:
6934:
6932:
6920:
6916:
6907:
6903:
6901:
6898:
6897:
6871:
6867:
6858:
6854:
6842:
6838:
6823:
6819:
6801:
6797:
6795:
6792:
6791:
6775:
6769:
6765:
6756:
6752:
6747:
6738:
6734:
6732:
6729:
6728:
6711:
6707:
6705:
6702:
6701:
6684:
6680:
6678:
6675:
6674:
6671:
6639:
6612:
6608:
6596:
6579:
6559:
6555:
6549:
6538:
6526:
6523:
6522:
6489:
6484:
6472:
6471:
6466:
6464:
6463:
6428:
6425:
6424:
6418:
6326:
6322:
6301:
6297:
6284:
6264:
6262:
6241:
6237:
6236:
6232:
6202:
6198:
6196:
6193:
6192:
6130:
6128:
6121:
6117:
6087:
6083:
6081:
6078:
6077:
6059:
6017:
6008:
6004:
5996:
5978:
5965:
5964:
5963:
5953:
5940:
5939:
5938:
5928:
5915:
5914:
5913:
5912:
5908:
5906:
5903:
5902:
5895:point estimates
5858:
5849:
5845:
5837:
5824:
5811:
5810:
5809:
5807:
5804:
5803:
5793:
5781:
5756:
5752:
5737:
5733:
5724:
5720:
5718:
5715:
5714:
5694:
5690:
5681:
5677:
5665:
5661:
5652:
5648:
5630:
5626:
5611:
5607:
5590:
5586:
5565:
5561:
5560:
5556:
5554:
5551:
5550:
5525:
5522:
5521:
5495:
5491:
5476:
5472:
5460:
5456:
5441:
5437:
5410:
5406:
5391:
5387:
5369:
5365:
5350:
5346:
5331:
5327:
5260:
5252:
5250:
5218:
5214:
5199:
5195:
5194:
5190:
5188:
5185:
5184:
5155:
5151:
5139:
5135:
5120:
5116:
5095:
5091:
5076:
5072:
5029:
5021:
5019:
4993:
4989:
4988:
4984:
4982:
4979:
4978:
4931:
4927:
4916:
4913:
4912:
4880:
4876:
4868:
4865:
4864:
4828:
4824:
4806:
4802:
4797:
4794:
4793:
4787:
4777:
4761:
4750:
4703:
4697:
4693:
4691:
4685:
4674:
4669:
4665:
4655:
4647:
4642:
4640:
4639:
4627:
4623:
4621:
4618:
4617:
4602:
4588:with parameter
4564:
4560:
4542:
4538:
4529:
4525:
4523:
4520:
4519:
4516:
4441:
4438:
4437:
4402:
4398:
4385:
4335:
4333:
4313:
4310:
4309:
4283:
4279:
4264:
4260:
4218:
4214:
4201:
4175:
4173:
4146:
4142:
4129:
4103:
4101:
4083:
4079:
4064:
4060:
4027:
4023:
3996:
3992:
3965:
3961:
3946:
3942:
3931:
3928:
3927:
3892:
3888:
3875:
3849:
3847:
3829:
3825:
3810:
3806:
3795:
3792:
3791:
3714:
3710:
3695:
3691:
3689:
3686:
3685:
3662:
3658:
3643:
3639:
3637:
3634:
3633:
3599:
3596:
3595:
3572:
3568:
3553:
3549:
3547:
3544:
3543:
3521:
3518:
3517:
3495:
3492:
3491:
3467:
3465:
3462:
3461:
3442:
3425:
3422:
3421:
3394:
3390:
3375:
3371:
3363:
3360:
3359:
3316:
3312:
3297:
3293:
3284:
3280:
3263:
3259:
3238:
3234:
3219:
3215:
3214:
3210:
3208:
3205:
3204:
3153:
3150:
3149:
3112:
3109:
3108:
3071:
3068:
3067:
3030:
3027:
3026:
2998:
2995:
2994:
2939:
2936:
2935:
2899:
2886:
2882:
2869:
2867:
2839:
2820:
2816:
2803:
2801:
2779:
2767:
2763:
2761:
2723:
2719:
2704:
2700:
2699:
2695:
2693:
2690:
2689:
2684:
2673:
2651:Similarly, for
2649:
2607:
2603:
2558:
2554:
2514:
2506:
2504:
2502:
2499:
2498:
2454:
2451:
2450:
2413:
2410:
2409:
2381:
2378:
2377:
2345:
2341:
2330:
2327:
2326:
2271:
2267:
2265:
2262:
2261:
2233:
2194:
2190:
2188:
2185:
2184:
2147:
2143:
2119:
2115:
2075:
2067:
2065:
2039:
2035:
2034:
2030:
2028:
2025:
2024:
1998:
1994:
1992:
1989:
1988:
1959:
1955:
1946:
1942:
1927:
1923:
1921:
1918:
1917:
1896:
1892:
1877:
1873:
1871:
1868:
1867:
1847:
1843:
1834:
1830:
1821:
1817:
1815:
1812:
1811:
1794:
1790:
1788:
1785:
1784:
1763:
1759:
1744:
1740:
1731:
1727:
1725:
1722:
1721:
1695:
1690:
1665:
1661:
1646:
1642:
1605:
1601:
1586:
1582:
1540:
1536:
1535:
1531:
1529:
1526:
1525:
1505:
1501:
1486:
1482:
1457:
1453:
1438:
1434:
1392:
1388:
1387:
1383:
1381:
1378:
1377:
1345:
1341:
1326:
1322:
1301:
1297:
1282:
1278:
1260:
1256:
1216:
1208:
1206:
1180:
1176:
1175:
1171:
1169:
1166:
1165:
1136:
1132:
1117:
1113:
1098:
1094:
1079:
1075:
1065:
1052:
1051:
1050:
1044:
1033:
1003:
999:
998:
994:
992:
989:
988:
955:
951:
949:
946:
945:
942:
904:
895:
880:
871:
864:
854:
845:
834:
826:
822:
818:
809:
802:
794:
760:
756:
754:
751:
750:
727:
723:
721:
718:
717:
707:
697:
668:
664:
662:
659:
658:
652:
641:
631:
591:
587:
572:
568:
555:
551:
536:
532:
510:
509:
507:
504:
503:
469:
465:
450:
446:
424:
420:
418:
415:
414:
396:
395:
389:
362:
358:
343:
339:
317:
313:
311:
308:
307:
282:
281:
273:
271:
235:
231:
204:
200:
173:
169:
142:
138:
136:
133:
132:
118:
60:rank statistics
48:order statistic
17:
12:
11:
5:
12721:
12711:
12710:
12705:
12700:
12683:
12682:
12680:
12679:
12667:
12655:
12641:
12628:
12625:
12624:
12621:
12620:
12617:
12616:
12614:
12613:
12608:
12603:
12598:
12593:
12587:
12585:
12579:
12578:
12576:
12575:
12570:
12565:
12560:
12555:
12550:
12545:
12540:
12535:
12530:
12524:
12522:
12516:
12515:
12513:
12512:
12507:
12502:
12493:
12488:
12483:
12477:
12475:
12469:
12468:
12466:
12465:
12460:
12455:
12446:
12444:Bioinformatics
12440:
12438:
12428:
12427:
12415:
12414:
12411:
12410:
12407:
12406:
12403:
12402:
12400:
12399:
12393:
12391:
12387:
12386:
12384:
12383:
12377:
12375:
12369:
12368:
12366:
12365:
12360:
12355:
12350:
12344:
12342:
12333:
12327:
12326:
12323:
12322:
12320:
12319:
12314:
12309:
12304:
12299:
12293:
12291:
12285:
12284:
12282:
12281:
12276:
12271:
12263:
12258:
12253:
12252:
12251:
12249:partial (PACF)
12240:
12238:
12232:
12231:
12229:
12228:
12223:
12218:
12210:
12205:
12199:
12197:
12196:Specific tests
12193:
12192:
12190:
12189:
12184:
12179:
12174:
12169:
12164:
12159:
12154:
12148:
12146:
12139:
12133:
12132:
12130:
12129:
12128:
12127:
12126:
12125:
12110:
12109:
12108:
12098:
12096:Classification
12093:
12088:
12083:
12078:
12073:
12068:
12062:
12060:
12054:
12053:
12051:
12050:
12045:
12043:McNemar's test
12040:
12035:
12030:
12025:
12019:
12017:
12007:
12006:
11982:
11981:
11978:
11977:
11974:
11973:
11971:
11970:
11965:
11960:
11955:
11949:
11947:
11941:
11940:
11938:
11937:
11921:
11915:
11913:
11907:
11906:
11904:
11903:
11898:
11893:
11888:
11883:
11881:Semiparametric
11878:
11873:
11867:
11865:
11861:
11860:
11858:
11857:
11852:
11847:
11842:
11836:
11834:
11828:
11827:
11825:
11824:
11819:
11814:
11809:
11804:
11798:
11796:
11790:
11789:
11787:
11786:
11781:
11776:
11771:
11765:
11763:
11753:
11752:
11749:
11748:
11743:
11737:
11729:
11728:
11725:
11724:
11721:
11720:
11718:
11717:
11716:
11715:
11705:
11700:
11695:
11694:
11693:
11688:
11677:
11675:
11669:
11668:
11665:
11664:
11662:
11661:
11656:
11655:
11654:
11646:
11638:
11622:
11619:(MannâWhitney)
11614:
11613:
11612:
11599:
11598:
11597:
11586:
11584:
11578:
11577:
11575:
11574:
11573:
11572:
11567:
11562:
11552:
11547:
11544:(ShapiroâWilk)
11539:
11534:
11529:
11524:
11519:
11511:
11505:
11503:
11497:
11496:
11494:
11493:
11485:
11476:
11464:
11458:
11456:Specific tests
11452:
11451:
11448:
11447:
11445:
11444:
11439:
11434:
11428:
11426:
11420:
11419:
11417:
11416:
11411:
11410:
11409:
11399:
11398:
11397:
11387:
11381:
11379:
11373:
11372:
11370:
11369:
11368:
11367:
11362:
11352:
11347:
11342:
11337:
11332:
11326:
11324:
11318:
11317:
11315:
11314:
11309:
11308:
11307:
11302:
11301:
11300:
11295:
11280:
11279:
11278:
11273:
11268:
11263:
11252:
11250:
11241:
11235:
11234:
11232:
11231:
11226:
11221:
11220:
11219:
11209:
11204:
11203:
11202:
11192:
11191:
11190:
11185:
11180:
11170:
11165:
11160:
11159:
11158:
11153:
11148:
11132:
11131:
11130:
11125:
11120:
11110:
11109:
11108:
11103:
11093:
11092:
11091:
11081:
11080:
11079:
11069:
11064:
11059:
11053:
11051:
11041:
11040:
11028:
11027:
11024:
11023:
11020:
11019:
11017:
11016:
11011:
11006:
11001:
10995:
10993:
10987:
10986:
10984:
10983:
10978:
10973:
10967:
10965:
10961:
10960:
10958:
10957:
10952:
10947:
10942:
10937:
10932:
10927:
10921:
10919:
10913:
10912:
10910:
10909:
10907:Standard error
10904:
10899:
10894:
10893:
10892:
10887:
10876:
10874:
10868:
10867:
10865:
10864:
10859:
10854:
10849:
10844:
10839:
10837:Optimal design
10834:
10829:
10823:
10821:
10811:
10810:
10798:
10797:
10794:
10793:
10790:
10789:
10787:
10786:
10781:
10776:
10771:
10766:
10761:
10756:
10751:
10746:
10741:
10736:
10731:
10726:
10721:
10716:
10710:
10708:
10702:
10701:
10699:
10698:
10693:
10692:
10691:
10686:
10676:
10671:
10665:
10663:
10657:
10656:
10654:
10653:
10648:
10643:
10637:
10635:
10634:Summary tables
10631:
10630:
10628:
10627:
10621:
10619:
10613:
10612:
10609:
10608:
10606:
10605:
10604:
10603:
10598:
10593:
10583:
10577:
10575:
10569:
10568:
10566:
10565:
10560:
10555:
10550:
10545:
10540:
10535:
10529:
10527:
10521:
10520:
10518:
10517:
10512:
10507:
10506:
10505:
10500:
10495:
10490:
10485:
10480:
10475:
10470:
10468:Contraharmonic
10465:
10460:
10449:
10447:
10438:
10428:
10427:
10415:
10414:
10412:
10411:
10406:
10400:
10397:
10396:
10389:
10388:
10381:
10374:
10366:
10360:
10359:
10353:
10333:
10321:
10320:External links
10318:
10315:
10314:
10308:
10282:
10253:(1): 148â164.
10243:Willcox, Karen
10233:
10224:
10204:(4): 377â408.
10179:
10152:
10139:(3): 191â231.
10114:
10108:
10082:
10044:
10037:
10014:
10007:
9987:
9980:
9953:
9952:
9950:
9947:
9944:
9943:
9898:
9896:
9889:
9884:
9883:
9878:
9873:
9868:
9863:
9858:
9853:
9848:
9841:
9838:
9837:
9836:
9831:
9826:
9820:
9815:
9809:
9804:
9799:
9797:BRS-inequality
9794:
9789:
9782:
9779:
9743:
9740:
9739:
9738:
9723:
9719:
9713:
9710:
9707:
9703:
9699:
9696:
9693:
9690:
9687:
9684:
9681:
9678:
9675:
9672:
9667:
9663:
9659:
9656:
9653:
9650:
9647:
9644:
9641:
9638:
9635:
9632:
9629:
9626:
9623:
9618:
9615:
9612:
9608:
9604:
9601:
9598:
9595:
9592:
9587:
9583:
9579:
9576:
9573:
9570:
9567:
9564:
9561:
9557:
9550:
9545:
9542:
9537:
9529:
9526:
9523:
9518:
9515:
9512:
9508:
9504:
9501:
9499:
9497:
9494:
9490:
9484:
9481:
9478:
9474:
9468:
9464:
9460:
9455:
9451:
9445:
9441:
9437:
9432:
9428:
9424:
9421:
9416:
9413:
9410:
9406:
9400:
9396:
9392:
9387:
9383:
9379:
9374:
9369:
9365:
9360:
9353:
9348:
9345:
9340:
9332:
9329:
9326:
9321:
9318:
9315:
9311:
9307:
9304:
9302:
9300:
9297:
9294:
9291:
9288:
9283:
9280:
9277:
9273:
9269:
9266:
9263:
9260:
9257:
9254:
9249:
9246:
9243:
9239:
9235:
9232:
9229:
9226:
9224:
9222:
9219:
9216:
9211:
9208:
9205:
9201:
9197:
9194:
9191:
9190:
9165:
9162:
9159:
9155:
9143:
9142:
9127:
9122:
9119:
9116:
9112:
9106:
9102:
9098:
9093:
9089:
9083:
9079:
9075:
9070:
9066:
9062:
9056:
9051:
9048:
9043:
9035:
9032:
9029:
9024:
9021:
9018:
9014:
9010:
9007:
9005:
9003:
9000:
8997:
8994:
8986:
8983:
8980:
8972:
8969:
8966:
8963:
8961:
8959:
8956:
8953:
8950:
8942:
8934:
8931:
8928:
8925:
8923:
8921:
8918:
8915:
8910:
8907:
8904:
8900:
8896:
8893:
8890:
8889:
8866:
8863:
8860:
8855:
8852:
8849:
8845:
8841:
8838:
8827:
8826:
8811:
8806:
8803:
8800:
8796:
8790:
8786:
8782:
8777:
8773:
8769:
8764:
8759:
8755:
8748:
8743:
8740:
8735:
8727:
8724:
8721:
8716:
8713:
8710:
8706:
8702:
8699:
8697:
8695:
8692:
8689:
8686:
8678:
8675:
8672:
8664:
8661:
8658:
8655:
8653:
8651:
8648:
8645:
8642:
8634:
8626:
8623:
8620:
8617:
8615:
8613:
8610:
8607:
8602:
8599:
8596:
8592:
8588:
8585:
8582:
8581:
8552:
8540:
8539:
8528:
8525:
8522:
8519:
8516:
8513:
8510:
8507:
8504:
8501:
8498:
8495:
8492:
8489:
8486:
8481:
8477:
8468:
8465:
8462:
8459:
8456:
8453:
8450:
8447:
8444:
8441:
8438:
8435:
8432:
8427:
8423:
8416:
8413:
8410:
8407:
8404:
8401:
8398:
8395:
8392:
8389:
8386:
8383:
8380:
8377:
8374:
8371:
8368:
8365:
8360:
8356:
8326:
8305:
8302:
8299:
8296:
8273:
8270:
8267:
8264:
8242:
8238:
8234:
8231:
8228:
8223:
8219:
8215:
8210:
8206:
8193:
8190:
8159:
8156:
8121:
8117:
8113:
8108:
8104:
8100:
8097:
8094:
8091:
8087:
8082:
8077:
8070:
8067:
8060:
8055:
8051:
8026:
8022:
8016:
8013:
8009:
7999:
7995:
7989:
7986:
7983:
7979:
7975:
7970:
7966:
7962:
7957:
7953:
7928:
7906:
7902:
7879:
7876:
7872:
7846:
7842:
7838:
7835:
7832:
7829:
7803:
7800:
7797:
7794:
7791:
7765:
7762:
7737:
7733:
7710:
7706:
7683:
7680:
7676:
7653:
7649:
7645:
7640:
7636:
7611:
7607:
7603:
7598:
7593:
7589:
7568:
7563:
7560:
7557:
7553:
7549:
7546:
7543:
7540:
7535:
7531:
7520:
7505:
7500:
7497:
7494:
7490:
7484:
7477:
7474:
7467:
7447:
7444:
7441:
7438:
7435:
7432:
7429:
7407:
7402:
7399:
7396:
7392:
7386:
7382:
7378:
7369:observations.
7358:
7348:
7329:
7325:
7321:
7318:
7315:
7312:
7309:
7306:
7303:
7300:
7297:
7294:
7291:
7288:
7285:
7280:
7276:
7253:
7249:
7228:
7217:
7216:
7205:
7202:
7198:
7195:
7192:
7187:
7184:
7181:
7177:
7173:
7170:
7167:
7163:
7160:
7154:
7149:
7145:
7138:
7135:
7132:
7129:
7126:
7123:
7120:
7117:
7114:
7111:
7107:
7102:
7096:
7093:
7090:
7087:
7084:
7081:
7078:
7075:
7072:
7068:
7063:
7060:
7055:
7052:
7049:
7045:
7041:
7038:
7015:
6993:
6990:
6987:
6983:
6957:
6953:
6950:
6947:
6942:
6938:
6931:
6928:
6923:
6919:
6915:
6910:
6906:
6885:
6882:
6879:
6874:
6870:
6866:
6861:
6857:
6853:
6850:
6845:
6841:
6837:
6834:
6831:
6826:
6822:
6818:
6815:
6812:
6809:
6804:
6800:
6778:
6772:
6768:
6764:
6759:
6755:
6750:
6746:
6741:
6737:
6714:
6710:
6687:
6683:
6670:
6667:
6637:
6632:
6631:
6620:
6615:
6611:
6605:
6602:
6599:
6594:
6591:
6588:
6585:
6582:
6578:
6574:
6571:
6567:
6562:
6558:
6552:
6547:
6544:
6541:
6537:
6533:
6530:
6516:
6515:
6504:
6498:
6495:
6492:
6488:
6475:
6469:
6459:
6456:
6453:
6450:
6447:
6444:
6441:
6438:
6435:
6432:
6417:
6414:
6351:
6350:
6338:
6329:
6325:
6321:
6318:
6315:
6312:
6307:
6304:
6300:
6296:
6293:
6290:
6287:
6282:
6279:
6276:
6273:
6270:
6267:
6261:
6258:
6255:
6252:
6247:
6244:
6240:
6235:
6231:
6228:
6225:
6220:
6217:
6214:
6211:
6208:
6205:
6201:
6174:
6173:
6162:
6158:
6152:
6148:
6145:
6142:
6139:
6136:
6133:
6127:
6124:
6120:
6116:
6113:
6110:
6105:
6102:
6099:
6096:
6093:
6090:
6086:
6058:
6055:
6050:
6049:
6038:
6035:
6032:
6029:
6024:
6021:
6016:
6011:
6007:
6003:
5999:
5995:
5992:
5988:
5981:
5976:
5973:
5968:
5962:
5956:
5951:
5948:
5943:
5937:
5931:
5926:
5923:
5918:
5911:
5891:
5890:
5879:
5876:
5873:
5870:
5865:
5862:
5857:
5852:
5848:
5844:
5840:
5836:
5833:
5827:
5822:
5819:
5814:
5792:
5789:
5780:
5777:
5776:
5775:
5764:
5759:
5755:
5751:
5748:
5745:
5740:
5736:
5732:
5727:
5723:
5702:
5697:
5693:
5689:
5684:
5680:
5676:
5673:
5668:
5664:
5660:
5655:
5651:
5647:
5644:
5641:
5638:
5633:
5629:
5625:
5622:
5619:
5614:
5610:
5606:
5599:
5596:
5593:
5589:
5585:
5582:
5579:
5574:
5571:
5568:
5564:
5559:
5547:
5546:
5535:
5532:
5529:
5509:
5506:
5503:
5498:
5494:
5490:
5487:
5484:
5479:
5475:
5469:
5466:
5463:
5459:
5455:
5452:
5449:
5444:
5440:
5436:
5433:
5430:
5425:
5422:
5419:
5416:
5413:
5409:
5405:
5402:
5399:
5394:
5390:
5386:
5383:
5380:
5377:
5372:
5368:
5364:
5359:
5356:
5353:
5349:
5345:
5342:
5339:
5334:
5330:
5326:
5320:
5317:
5314:
5311:
5308:
5305:
5302:
5299:
5296:
5293:
5290:
5287:
5284:
5281:
5278:
5275:
5272:
5269:
5266:
5263:
5258:
5255:
5249:
5246:
5243:
5240:
5237:
5234:
5227:
5224:
5221:
5217:
5213:
5208:
5205:
5202:
5198:
5193:
5181:
5180:
5169:
5166:
5163:
5158:
5154:
5148:
5145:
5142:
5138:
5134:
5131:
5128:
5123:
5119:
5115:
5112:
5109:
5104:
5101:
5098:
5094:
5090:
5087:
5084:
5079:
5075:
5071:
5065:
5062:
5059:
5056:
5053:
5050:
5047:
5044:
5041:
5038:
5035:
5032:
5027:
5024:
5018:
5015:
5012:
5009:
5002:
4999:
4996:
4992:
4987:
4964:
4963:
4952:
4949:
4945:
4942:
4939:
4934:
4930:
4926:
4923:
4920:
4906:
4905:
4894:
4891:
4888:
4883:
4879:
4875:
4872:
4849:
4846:
4842:
4839:
4836:
4831:
4827:
4823:
4820:
4817:
4814:
4809:
4805:
4801:
4783:
4776:
4773:
4760:
4757:
4746:
4740:
4739:
4738:
4737:
4725:
4718:
4715:
4712:
4709:
4706:
4700:
4696:
4688:
4683:
4680:
4677:
4673:
4668:
4662:
4659:
4650:
4645:
4636:
4633:
4630:
4626:
4607:= 1,2,3, ...,
4596:
4567:
4563:
4559:
4556:
4553:
4550:
4545:
4541:
4537:
4532:
4528:
4515:
4512:
4499:
4496:
4493:
4490:
4487:
4484:
4481:
4478:
4475:
4472:
4469:
4466:
4463:
4460:
4457:
4454:
4451:
4448:
4445:
4422:
4419:
4416:
4413:
4410:
4405:
4401:
4397:
4394:
4391:
4388:
4383:
4380:
4377:
4374:
4371:
4368:
4365:
4362:
4359:
4356:
4353:
4350:
4347:
4344:
4341:
4338:
4332:
4329:
4326:
4323:
4320:
4317:
4297:
4292:
4289:
4286:
4282:
4278:
4273:
4270:
4267:
4263:
4259:
4256:
4253:
4250:
4247:
4244:
4238:
4235:
4232:
4229:
4226:
4221:
4217:
4213:
4210:
4207:
4204:
4199:
4196:
4193:
4190:
4187:
4184:
4181:
4178:
4172:
4166:
4163:
4160:
4157:
4154:
4149:
4145:
4141:
4138:
4135:
4132:
4127:
4124:
4121:
4118:
4115:
4112:
4109:
4106:
4100:
4097:
4092:
4089:
4086:
4082:
4078:
4073:
4070:
4067:
4063:
4059:
4056:
4053:
4050:
4047:
4044:
4041:
4036:
4033:
4030:
4026:
4022:
4019:
4016:
4013:
4010:
4005:
4002:
3999:
3995:
3991:
3988:
3985:
3982:
3979:
3974:
3971:
3968:
3964:
3960:
3955:
3952:
3949:
3945:
3941:
3938:
3935:
3912:
3909:
3906:
3903:
3900:
3895:
3891:
3887:
3884:
3881:
3878:
3873:
3870:
3867:
3864:
3861:
3858:
3855:
3852:
3846:
3843:
3838:
3835:
3832:
3828:
3824:
3819:
3816:
3813:
3809:
3805:
3802:
3799:
3779:
3776:
3773:
3770:
3767:
3764:
3761:
3758:
3755:
3752:
3749:
3746:
3743:
3740:
3737:
3734:
3731:
3728:
3723:
3720:
3717:
3713:
3709:
3704:
3701:
3698:
3694:
3671:
3668:
3665:
3661:
3657:
3652:
3649:
3646:
3642:
3621:
3618:
3615:
3612:
3609:
3606:
3603:
3581:
3578:
3575:
3571:
3567:
3562:
3559:
3556:
3552:
3528:
3525:
3505:
3502:
3499:
3477:
3474:
3471:
3449:
3445:
3441:
3438:
3435:
3432:
3429:
3418:BRS-inequality
3405:
3402:
3397:
3393:
3389:
3386:
3383:
3378:
3374:
3370:
3367:
3348:
3347:
3336:
3333:
3330:
3327:
3324:
3319:
3315:
3311:
3308:
3305:
3300:
3296:
3292:
3287:
3283:
3279:
3272:
3269:
3266:
3262:
3258:
3255:
3252:
3247:
3244:
3241:
3237:
3233:
3228:
3225:
3222:
3218:
3213:
3189:respectively.
3178:
3175:
3172:
3169:
3166:
3163:
3160:
3157:
3137:
3134:
3131:
3128:
3125:
3122:
3119:
3116:
3096:
3093:
3090:
3087:
3084:
3081:
3078:
3075:
3055:
3052:
3049:
3046:
3043:
3040:
3037:
3034:
3014:
3011:
3008:
3005:
3002:
2962:
2959:
2956:
2952:
2949:
2946:
2943:
2932:
2931:
2917:
2914:
2911:
2908:
2905:
2902:
2895:
2892:
2889:
2885:
2881:
2878:
2875:
2872:
2863:
2860:
2857:
2854:
2851:
2848:
2845:
2842:
2835:
2832:
2829:
2826:
2823:
2819:
2815:
2812:
2809:
2806:
2797:
2794:
2791:
2788:
2785:
2782:
2776:
2773:
2770:
2766:
2760:
2757:
2754:
2751:
2748:
2745:
2742:
2739:
2732:
2729:
2726:
2722:
2718:
2713:
2710:
2707:
2703:
2698:
2678:
2667:
2648:
2645:
2630:
2629:
2616:
2613:
2610:
2606:
2602:
2599:
2596:
2593:
2590:
2587:
2584:
2581:
2578:
2575:
2572:
2567:
2564:
2561:
2557:
2550:
2547:
2544:
2541:
2538:
2535:
2532:
2529:
2526:
2523:
2520:
2517:
2512:
2509:
2479:
2476:
2473:
2470:
2467:
2464:
2461:
2458:
2438:
2435:
2432:
2429:
2426:
2423:
2420:
2417:
2397:
2394:
2391:
2388:
2385:
2353:
2348:
2344:
2340:
2337:
2334:
2321: + d
2293:to be between
2280:
2277:
2274:
2270:
2258:
2257:
2246:
2243:
2240:
2236:
2232:
2229:
2226:
2223:
2220:
2217:
2214:
2211:
2208:
2203:
2200:
2197:
2193:
2170:
2169:
2156:
2153:
2150:
2146:
2142:
2139:
2136:
2133:
2128:
2125:
2122:
2118:
2111:
2108:
2105:
2102:
2099:
2096:
2093:
2090:
2087:
2084:
2081:
2078:
2073:
2070:
2064:
2061:
2058:
2055:
2048:
2045:
2042:
2038:
2033:
2007:
2004:
2001:
1997:
1973:
1968:
1965:
1962:
1958:
1954:
1949:
1945:
1941:
1936:
1933:
1930:
1926:
1899:
1895:
1891:
1888:
1885:
1880:
1876:
1855:
1850:
1846:
1842:
1837:
1833:
1829:
1824:
1820:
1797:
1793:
1766:
1762:
1758:
1755:
1752:
1747:
1743:
1739:
1734:
1730:
1694:
1691:
1689:
1686:
1682:
1681:
1668:
1664:
1660:
1657:
1654:
1649:
1645:
1641:
1638:
1635:
1632:
1629:
1626:
1623:
1620:
1617:
1614:
1608:
1604:
1600:
1597:
1594:
1589:
1585:
1580:
1577:
1574:
1571:
1568:
1565:
1562:
1559:
1556:
1549:
1546:
1543:
1539:
1534:
1522:
1521:
1508:
1504:
1500:
1497:
1494:
1489:
1485:
1481:
1478:
1475:
1472:
1469:
1466:
1460:
1456:
1452:
1449:
1446:
1441:
1437:
1432:
1429:
1426:
1423:
1420:
1417:
1414:
1411:
1408:
1401:
1398:
1395:
1391:
1386:
1371:
1370:
1359:
1354:
1351:
1348:
1344:
1340:
1337:
1334:
1329:
1325:
1321:
1318:
1315:
1310:
1307:
1304:
1300:
1296:
1293:
1290:
1285:
1281:
1277:
1274:
1271:
1268:
1263:
1259:
1252:
1249:
1246:
1243:
1240:
1237:
1234:
1231:
1228:
1225:
1222:
1219:
1214:
1211:
1205:
1202:
1199:
1196:
1189:
1186:
1183:
1179:
1174:
1159:
1158:
1145:
1142:
1139:
1135:
1131:
1128:
1125:
1120:
1116:
1112:
1109:
1106:
1101:
1097:
1093:
1090:
1087:
1082:
1078:
1074:
1068:
1063:
1060:
1055:
1047:
1042:
1039:
1036:
1032:
1028:
1025:
1022:
1019:
1012:
1009:
1006:
1002:
997:
969:
966:
963:
958:
954:
941:
938:
900:
893:
876:
869:
862:
850:
843:
828:
824:
820:
814:
807:
800:
793:
790:
775:
772:
769:
766:
763:
759:
736:
733:
730:
726:
683:
680:
677:
674:
671:
667:
617:
616:
605:
600:
597:
594:
590:
586:
581:
578:
575:
571:
567:
564:
558:
554:
550:
547:
544:
539:
535:
530:
525:
522:
519:
516:
513:
493:
492:
481:
478:
472:
468:
464:
461:
458:
453:
449:
444:
441:
438:
433:
430:
427:
423:
383:
382:
371:
365:
361:
357:
354:
351:
346:
342:
337:
334:
331:
326:
323:
320:
316:
268:
267:
255:
252:
249:
244:
241:
238:
234:
224:
221:
218:
213:
210:
207:
203:
193:
190:
187:
182:
179:
176:
172:
162:
159:
156:
151:
148:
145:
141:
126:
125:
117:
114:
98:random samples
15:
9:
6:
4:
3:
2:
12720:
12709:
12706:
12704:
12701:
12699:
12696:
12695:
12693:
12678:
12677:
12668:
12666:
12665:
12656:
12654:
12653:
12648:
12642:
12640:
12639:
12630:
12629:
12626:
12612:
12609:
12607:
12606:Geostatistics
12604:
12602:
12599:
12597:
12594:
12592:
12589:
12588:
12586:
12584:
12580:
12574:
12573:Psychometrics
12571:
12569:
12566:
12564:
12561:
12559:
12556:
12554:
12551:
12549:
12546:
12544:
12541:
12539:
12536:
12534:
12531:
12529:
12526:
12525:
12523:
12521:
12517:
12511:
12508:
12506:
12503:
12501:
12497:
12494:
12492:
12489:
12487:
12484:
12482:
12479:
12478:
12476:
12474:
12470:
12464:
12461:
12459:
12456:
12454:
12450:
12447:
12445:
12442:
12441:
12439:
12437:
12436:Biostatistics
12433:
12429:
12425:
12420:
12416:
12398:
12397:Log-rank test
12395:
12394:
12392:
12388:
12382:
12379:
12378:
12376:
12374:
12370:
12364:
12361:
12359:
12356:
12354:
12351:
12349:
12346:
12345:
12343:
12341:
12337:
12334:
12332:
12328:
12318:
12315:
12313:
12310:
12308:
12305:
12303:
12300:
12298:
12295:
12294:
12292:
12290:
12286:
12280:
12277:
12275:
12272:
12270:
12268:(BoxâJenkins)
12264:
12262:
12259:
12257:
12254:
12250:
12247:
12246:
12245:
12242:
12241:
12239:
12237:
12233:
12227:
12224:
12222:
12221:DurbinâWatson
12219:
12217:
12211:
12209:
12206:
12204:
12203:DickeyâFuller
12201:
12200:
12198:
12194:
12188:
12185:
12183:
12180:
12178:
12177:Cointegration
12175:
12173:
12170:
12168:
12165:
12163:
12160:
12158:
12155:
12153:
12152:Decomposition
12150:
12149:
12147:
12143:
12140:
12138:
12134:
12124:
12121:
12120:
12119:
12116:
12115:
12114:
12111:
12107:
12104:
12103:
12102:
12099:
12097:
12094:
12092:
12089:
12087:
12084:
12082:
12079:
12077:
12074:
12072:
12069:
12067:
12064:
12063:
12061:
12059:
12055:
12049:
12046:
12044:
12041:
12039:
12036:
12034:
12031:
12029:
12026:
12024:
12023:Cohen's kappa
12021:
12020:
12018:
12016:
12012:
12008:
12004:
12000:
11996:
11992:
11987:
11983:
11969:
11966:
11964:
11961:
11959:
11956:
11954:
11951:
11950:
11948:
11946:
11942:
11936:
11932:
11928:
11922:
11920:
11917:
11916:
11914:
11912:
11908:
11902:
11899:
11897:
11894:
11892:
11889:
11887:
11884:
11882:
11879:
11877:
11876:Nonparametric
11874:
11872:
11869:
11868:
11866:
11862:
11856:
11853:
11851:
11848:
11846:
11843:
11841:
11838:
11837:
11835:
11833:
11829:
11823:
11820:
11818:
11815:
11813:
11810:
11808:
11805:
11803:
11800:
11799:
11797:
11795:
11791:
11785:
11782:
11780:
11777:
11775:
11772:
11770:
11767:
11766:
11764:
11762:
11758:
11754:
11747:
11744:
11742:
11739:
11738:
11734:
11730:
11714:
11711:
11710:
11709:
11706:
11704:
11701:
11699:
11696:
11692:
11689:
11687:
11684:
11683:
11682:
11679:
11678:
11676:
11674:
11670:
11660:
11657:
11653:
11647:
11645:
11639:
11637:
11631:
11630:
11629:
11626:
11625:Nonparametric
11623:
11621:
11615:
11611:
11608:
11607:
11606:
11600:
11596:
11595:Sample median
11593:
11592:
11591:
11588:
11587:
11585:
11583:
11579:
11571:
11568:
11566:
11563:
11561:
11558:
11557:
11556:
11553:
11551:
11548:
11546:
11540:
11538:
11535:
11533:
11530:
11528:
11525:
11523:
11520:
11518:
11516:
11512:
11510:
11507:
11506:
11504:
11502:
11498:
11492:
11490:
11486:
11484:
11482:
11477:
11475:
11470:
11466:
11465:
11462:
11459:
11457:
11453:
11443:
11440:
11438:
11435:
11433:
11430:
11429:
11427:
11425:
11421:
11415:
11412:
11408:
11405:
11404:
11403:
11400:
11396:
11393:
11392:
11391:
11388:
11386:
11383:
11382:
11380:
11378:
11374:
11366:
11363:
11361:
11358:
11357:
11356:
11353:
11351:
11348:
11346:
11343:
11341:
11338:
11336:
11333:
11331:
11328:
11327:
11325:
11323:
11319:
11313:
11310:
11306:
11303:
11299:
11296:
11294:
11291:
11290:
11289:
11286:
11285:
11284:
11281:
11277:
11274:
11272:
11269:
11267:
11264:
11262:
11259:
11258:
11257:
11254:
11253:
11251:
11249:
11245:
11242:
11240:
11236:
11230:
11227:
11225:
11222:
11218:
11215:
11214:
11213:
11210:
11208:
11205:
11201:
11200:loss function
11198:
11197:
11196:
11193:
11189:
11186:
11184:
11181:
11179:
11176:
11175:
11174:
11171:
11169:
11166:
11164:
11161:
11157:
11154:
11152:
11149:
11147:
11141:
11138:
11137:
11136:
11133:
11129:
11126:
11124:
11121:
11119:
11116:
11115:
11114:
11111:
11107:
11104:
11102:
11099:
11098:
11097:
11094:
11090:
11087:
11086:
11085:
11082:
11078:
11075:
11074:
11073:
11070:
11068:
11065:
11063:
11060:
11058:
11055:
11054:
11052:
11050:
11046:
11042:
11038:
11033:
11029:
11015:
11012:
11010:
11007:
11005:
11002:
11000:
10997:
10996:
10994:
10992:
10988:
10982:
10979:
10977:
10974:
10972:
10969:
10968:
10966:
10962:
10956:
10953:
10951:
10948:
10946:
10943:
10941:
10938:
10936:
10933:
10931:
10928:
10926:
10923:
10922:
10920:
10918:
10914:
10908:
10905:
10903:
10902:Questionnaire
10900:
10898:
10895:
10891:
10888:
10886:
10883:
10882:
10881:
10878:
10877:
10875:
10873:
10869:
10863:
10860:
10858:
10855:
10853:
10850:
10848:
10845:
10843:
10840:
10838:
10835:
10833:
10830:
10828:
10825:
10824:
10822:
10820:
10816:
10812:
10808:
10803:
10799:
10785:
10782:
10780:
10777:
10775:
10772:
10770:
10767:
10765:
10762:
10760:
10757:
10755:
10752:
10750:
10747:
10745:
10742:
10740:
10737:
10735:
10732:
10730:
10729:Control chart
10727:
10725:
10722:
10720:
10717:
10715:
10712:
10711:
10709:
10707:
10703:
10697:
10694:
10690:
10687:
10685:
10682:
10681:
10680:
10677:
10675:
10672:
10670:
10667:
10666:
10664:
10662:
10658:
10652:
10649:
10647:
10644:
10642:
10639:
10638:
10636:
10632:
10626:
10623:
10622:
10620:
10618:
10614:
10602:
10599:
10597:
10594:
10592:
10589:
10588:
10587:
10584:
10582:
10579:
10578:
10576:
10574:
10570:
10564:
10561:
10559:
10556:
10554:
10551:
10549:
10546:
10544:
10541:
10539:
10536:
10534:
10531:
10530:
10528:
10526:
10522:
10516:
10513:
10511:
10508:
10504:
10501:
10499:
10496:
10494:
10491:
10489:
10486:
10484:
10481:
10479:
10476:
10474:
10471:
10469:
10466:
10464:
10461:
10459:
10456:
10455:
10454:
10451:
10450:
10448:
10446:
10442:
10439:
10437:
10433:
10429:
10425:
10420:
10416:
10410:
10407:
10405:
10402:
10401:
10398:
10394:
10387:
10382:
10380:
10375:
10373:
10368:
10367:
10364:
10358:
10354:
10348:
10347:
10342:
10339:
10334:
10331:
10327:
10324:
10323:
10311:
10309:9780471722168
10305:
10301:
10297:
10293:
10286:
10278:
10274:
10270:
10266:
10261:
10256:
10252:
10248:
10244:
10237:
10228:
10212:
10207:
10203:
10199:
10198:
10193:
10189:
10183:
10175:
10171:
10167:
10163:
10156:
10147:
10142:
10138:
10134:
10133:
10128:
10124:
10123:Rényi, Alfréd
10118:
10111:
10109:9780471722168
10105:
10101:
10097:
10093:
10086:
10079:
10077:
10073:
10067:
10063:
10059:
10055:
10048:
10040:
10038:9780387981444
10034:
10030:
10029:
10021:
10019:
10010:
10008:9788131503942
10004:
10000:
9999:
9991:
9983:
9981:9780471722168
9977:
9973:
9969:
9965:
9958:
9954:
9940:
9937:
9929:
9926:December 2010
9919:
9915:
9909:
9908:
9902:
9897:
9888:
9887:
9882:
9879:
9877:
9874:
9872:
9869:
9867:
9864:
9862:
9859:
9857:
9854:
9852:
9849:
9847:
9844:
9843:
9835:
9832:
9830:
9827:
9824:
9821:
9819:
9816:
9813:
9810:
9808:
9805:
9803:
9800:
9798:
9795:
9793:
9790:
9788:
9785:
9784:
9778:
9776:
9772:
9768:
9764:
9759:
9753:
9749:
9721:
9717:
9711:
9708:
9705:
9694:
9688:
9685:
9679:
9673:
9665:
9654:
9648:
9645:
9639:
9633:
9630:
9627:
9621:
9616:
9613:
9610:
9599:
9593:
9585:
9574:
9568:
9565:
9562:
9555:
9543:
9540:
9527:
9524:
9521:
9516:
9513:
9510:
9506:
9502:
9500:
9492:
9488:
9482:
9479:
9476:
9466:
9462:
9453:
9443:
9439:
9435:
9430:
9426:
9419:
9414:
9411:
9408:
9398:
9394:
9390:
9385:
9381:
9372:
9367:
9363:
9358:
9346:
9343:
9330:
9327:
9324:
9319:
9316:
9313:
9309:
9305:
9303:
9295:
9289:
9286:
9278:
9271:
9264:
9261:
9255:
9252:
9244:
9237:
9230:
9227:
9225:
9217:
9214:
9206:
9199:
9192:
9181:
9180:
9179:
9160:
9153:
9125:
9120:
9117:
9114:
9104:
9100:
9091:
9081:
9077:
9073:
9068:
9064:
9049:
9046:
9033:
9030:
9027:
9022:
9019:
9016:
9012:
9008:
9006:
8998:
8992:
8984:
8981:
8978:
8967:
8964:
8962:
8954:
8948:
8940:
8929:
8926:
8924:
8916:
8913:
8905:
8898:
8891:
8880:
8879:
8878:
8861:
8858:
8850:
8843:
8836:
8809:
8804:
8801:
8798:
8788:
8784:
8780:
8775:
8771:
8762:
8757:
8753:
8741:
8738:
8725:
8722:
8719:
8714:
8711:
8708:
8704:
8700:
8698:
8690:
8684:
8676:
8673:
8670:
8659:
8656:
8654:
8646:
8640:
8632:
8621:
8618:
8616:
8608:
8605:
8597:
8590:
8583:
8572:
8571:
8570:
8550:
8526:
8520:
8514:
8511:
8508:
8505:
8499:
8496:
8493:
8487:
8484:
8479:
8475:
8466:
8460:
8454:
8451:
8445:
8442:
8439:
8433:
8430:
8425:
8421:
8414:
8408:
8402:
8399:
8393:
8387:
8384:
8378:
8375:
8372:
8366:
8363:
8358:
8354:
8346:
8345:
8344:
8324:
8300:
8294:
8287:
8268:
8262:
8240:
8236:
8232:
8229:
8226:
8221:
8217:
8213:
8208:
8204:
8189:
8187:
8182:
8178:
8154:
8144:
8140:
8119:
8115:
8106:
8102:
8098:
8095:
8089:
8085:
8080:
8075:
8065:
8058:
8053:
8049:
8024:
8020:
8014:
8011:
8007:
7997:
7993:
7987:
7984:
7981:
7977:
7973:
7968:
7964:
7960:
7955:
7951:
7942:
7926:
7904:
7900:
7877:
7874:
7870:
7861:
7844:
7840:
7833:
7830:
7827:
7820:
7816:
7801:
7795:
7792:
7789:
7782:
7760:
7735:
7731:
7723:subsets with
7708:
7704:
7681:
7678:
7674:
7651:
7647:
7643:
7638:
7634:
7626:3: Create an
7609:
7605:
7601:
7596:
7591:
7587:
7561:
7558:
7555:
7551:
7544:
7541:
7538:
7533:
7529:
7503:
7498:
7495:
7492:
7482:
7472:
7442:
7439:
7436:
7430:
7427:
7405:
7400:
7397:
7394:
7384:
7380:
7356:
7347:
7345:
7327:
7319:
7316:
7313:
7304:
7301:
7298:
7292:
7286:
7278:
7274:
7251:
7247:
7226:
7203:
7200:
7193:
7185:
7182:
7179:
7175:
7168:
7161:
7158:
7152:
7147:
7143:
7133:
7130:
7127:
7118:
7115:
7112:
7105:
7100:
7091:
7085:
7079:
7076:
7073:
7066:
7061:
7050:
7043:
7036:
7029:
7028:
7027:
7013:
6988:
6981:
6971:
6955:
6948:
6940:
6936:
6929:
6921:
6917:
6908:
6904:
6880:
6877:
6872:
6868:
6859:
6855:
6851:
6843:
6839:
6835:
6832:
6824:
6820:
6816:
6810:
6802:
6798:
6770:
6766:
6762:
6757:
6753:
6744:
6739:
6735:
6712:
6708:
6700:at the point
6685:
6681:
6666:
6664:
6660:
6656:
6652:
6648:
6644:
6640:
6618:
6613:
6609:
6603:
6600:
6597:
6592:
6589:
6586:
6583:
6580:
6576:
6572:
6569:
6565:
6560:
6556:
6550:
6545:
6542:
6539:
6535:
6531:
6528:
6521:
6520:
6519:
6502:
6496:
6493:
6490:
6486:
6467:
6454:
6451:
6448:
6445:
6442:
6439:
6436:
6430:
6423:
6422:
6421:
6413:
6411:
6407:
6403:
6399:
6395:
6391:
6386:
6384:
6380:
6376:
6372:
6368:
6364:
6360:
6356:
6336:
6327:
6313:
6305:
6302:
6298:
6291:
6285:
6277:
6274:
6271:
6265:
6259:
6253:
6245:
6242:
6238:
6233:
6229:
6226:
6223:
6212:
6209:
6199:
6191:
6190:
6189:
6187:
6183:
6179:
6160:
6156:
6150:
6143:
6140:
6137:
6131:
6125:
6122:
6118:
6114:
6111:
6108:
6097:
6094:
6084:
6076:
6075:
6074:
6072:
6068:
6064:
6054:
6036:
6030:
6027:
6022:
6019:
6014:
6009:
6001:
5997:
5993:
5986:
5974:
5971:
5960:
5949:
5946:
5935:
5924:
5921:
5909:
5901:
5900:
5899:
5896:
5877:
5871:
5868:
5863:
5860:
5855:
5850:
5842:
5838:
5834:
5820:
5817:
5802:
5801:
5800:
5796:
5788:
5786:
5762:
5757:
5753:
5749:
5746:
5743:
5738:
5734:
5730:
5725:
5721:
5695:
5691:
5682:
5678:
5674:
5666:
5662:
5653:
5649:
5645:
5642:
5639:
5631:
5627:
5623:
5620:
5617:
5612:
5608:
5594:
5587:
5583:
5580:
5577:
5569:
5562:
5557:
5549:
5548:
5533:
5530:
5527:
5504:
5496:
5492:
5485:
5477:
5473:
5467:
5464:
5461:
5450:
5442:
5438:
5434:
5431:
5423:
5420:
5417:
5414:
5411:
5400:
5392:
5388:
5384:
5378:
5370:
5366:
5357:
5354:
5351:
5340:
5332:
5328:
5318:
5312:
5309:
5306:
5300:
5294:
5291:
5288:
5285:
5282:
5276:
5270:
5267:
5264:
5256:
5253:
5247:
5241:
5238:
5235:
5222:
5215:
5211:
5203:
5196:
5191:
5183:
5182:
5164:
5156:
5152:
5146:
5143:
5140:
5129:
5121:
5117:
5113:
5110:
5102:
5099:
5096:
5085:
5077:
5073:
5063:
5057:
5054:
5051:
5045:
5039:
5036:
5033:
5025:
5022:
5016:
5010:
4997:
4990:
4985:
4977:
4976:
4975:
4973:
4969:
4950:
4947:
4940:
4932:
4928:
4924:
4921:
4918:
4911:
4910:
4909:
4889:
4881:
4877:
4873:
4870:
4863:
4862:
4861:
4847:
4844:
4837:
4829:
4825:
4821:
4815:
4807:
4803:
4799:
4791:
4786:
4782:
4772:
4770:
4766:
4756:
4754:
4749:
4745:
4723:
4716:
4713:
4710:
4707:
4704:
4698:
4694:
4686:
4681:
4678:
4675:
4671:
4666:
4660:
4657:
4648:
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4631:
4624:
4616:
4615:
4614:
4613:
4612:
4610:
4606:
4600:
4595:
4591:
4587:
4583:
4565:
4561:
4557:
4554:
4551:
4548:
4543:
4539:
4535:
4530:
4526:
4511:
4494:
4491:
4485:
4482:
4479:
4473:
4470:
4467:
4464:
4461:
4458:
4452:
4449:
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4443:
4417:
4414:
4411:
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4395:
4392:
4389:
4378:
4375:
4369:
4366:
4363:
4357:
4354:
4345:
4342:
4339:
4330:
4324:
4318:
4315:
4287:
4280:
4276:
4268:
4261:
4254:
4251:
4248:
4245:
4242:
4233:
4230:
4227:
4219:
4211:
4208:
4205:
4194:
4191:
4188:
4185:
4182:
4176:
4170:
4161:
4158:
4155:
4147:
4139:
4136:
4133:
4122:
4119:
4116:
4113:
4110:
4104:
4098:
4087:
4080:
4076:
4068:
4061:
4054:
4051:
4048:
4045:
4042:
4031:
4024:
4017:
4014:
4011:
4000:
3993:
3986:
3983:
3980:
3969:
3962:
3958:
3950:
3943:
3936:
3933:
3907:
3904:
3901:
3893:
3885:
3882:
3879:
3868:
3865:
3862:
3859:
3856:
3850:
3844:
3833:
3826:
3822:
3814:
3807:
3800:
3797:
3774:
3771:
3765:
3762:
3759:
3753:
3750:
3747:
3744:
3741:
3738:
3732:
3729:
3726:
3718:
3711:
3707:
3699:
3692:
3666:
3659:
3655:
3647:
3640:
3619:
3616:
3613:
3610:
3607:
3604:
3601:
3576:
3569:
3565:
3557:
3550:
3540:
3526:
3523:
3503:
3500:
3497:
3475:
3472:
3469:
3447:
3443:
3439:
3436:
3433:
3430:
3427:
3419:
3403:
3400:
3395:
3391:
3387:
3384:
3381:
3376:
3372:
3368:
3365:
3357:
3353:
3334:
3331:
3328:
3325:
3317:
3313:
3309:
3306:
3303:
3298:
3294:
3290:
3285:
3281:
3267:
3260:
3256:
3253:
3250:
3242:
3235:
3231:
3223:
3216:
3211:
3203:
3202:
3201:
3199:
3195:
3190:
3173:
3170:
3167:
3164:
3161:
3158:
3132:
3129:
3126:
3123:
3120:
3117:
3091:
3088:
3085:
3082:
3079:
3076:
3050:
3047:
3044:
3041:
3038:
3035:
3009:
3006:
3003:
2992:
2989: â
2988:
2984:
2980:
2976:
2957:
2954:
2950:
2947:
2941:
2915:
2909:
2906:
2903:
2893:
2890:
2887:
2879:
2876:
2873:
2861:
2855:
2852:
2849:
2846:
2843:
2833:
2830:
2827:
2824:
2821:
2813:
2810:
2807:
2795:
2789:
2786:
2783:
2774:
2771:
2768:
2764:
2758:
2755:
2752:
2746:
2743:
2740:
2727:
2720:
2716:
2708:
2701:
2696:
2688:
2687:
2686:
2682:
2677:
2671:
2666:
2662:
2658:
2654:
2644:
2642:
2638:
2633:
2614:
2611:
2608:
2600:
2597:
2594:
2591:
2588:
2585:
2579:
2576:
2573:
2570:
2565:
2562:
2559:
2555:
2548:
2542:
2539:
2536:
2530:
2524:
2521:
2518:
2510:
2507:
2497:
2496:
2495:
2494:for details)
2493:
2474:
2471:
2468:
2465:
2462:
2459:
2433:
2430:
2427:
2424:
2421:
2418:
2392:
2389:
2386:
2375:
2372: â
2371:
2367:
2346:
2342:
2338:
2332:
2324:
2320:
2316:
2312:
2308:
2304:
2301: +
2300:
2296:
2275:
2268:
2244:
2238:
2230:
2227:
2224:
2221:
2218:
2212:
2209:
2206:
2198:
2191:
2183:
2182:
2181:
2179:
2175:
2172:that is, the
2154:
2151:
2148:
2140:
2137:
2134:
2126:
2123:
2120:
2116:
2109:
2103:
2100:
2097:
2091:
2085:
2082:
2079:
2071:
2068:
2062:
2056:
2043:
2036:
2031:
2023:
2022:
2021:
2002:
1995:
1985:
1963:
1956:
1947:
1943:
1939:
1931:
1924:
1915:
1897:
1893:
1889:
1886:
1883:
1878:
1874:
1848:
1844:
1835:
1831:
1827:
1822:
1818:
1795:
1791:
1782:
1781:random sample
1764:
1760:
1756:
1753:
1750:
1745:
1741:
1737:
1732:
1728:
1718:
1716:
1712:
1708:
1704:
1703:unit interval
1700:
1685:
1666:
1655:
1647:
1643:
1639:
1636:
1630:
1627:
1624:
1618:
1615:
1606:
1602:
1598:
1595:
1592:
1587:
1583:
1569:
1566:
1563:
1557:
1544:
1537:
1532:
1524:
1523:
1506:
1495:
1487:
1483:
1476:
1470:
1467:
1458:
1454:
1450:
1447:
1444:
1439:
1435:
1421:
1418:
1415:
1409:
1396:
1389:
1384:
1376:
1375:
1374:
1357:
1352:
1349:
1346:
1335:
1327:
1323:
1319:
1316:
1308:
1305:
1302:
1291:
1283:
1279:
1269:
1261:
1257:
1250:
1244:
1241:
1238:
1232:
1226:
1223:
1220:
1212:
1209:
1203:
1197:
1184:
1177:
1172:
1164:
1163:
1162:
1143:
1140:
1137:
1126:
1118:
1114:
1110:
1107:
1099:
1088:
1080:
1076:
1061:
1058:
1045:
1040:
1037:
1034:
1030:
1026:
1020:
1007:
1000:
995:
987:
986:
985:
983:
964:
956:
952:
937:
935:
931:
927:
923:
918:
916:
912:
908:
903:
899:
892:
888:
884:
879:
875:
868:
861:
856:
853:
849:
842:
838:
832:
817:
813:
806:
799:
789:
770:
767:
764:
757:
731:
724:
714:
710:
705:
700:
678:
675:
672:
665:
655:
648:
644:
639:
634:
628:
626:
622:
603:
595:
588:
584:
576:
569:
565:
556:
552:
548:
545:
542:
537:
533:
502:
501:
500:
498:
479:
470:
466:
462:
459:
456:
451:
447:
436:
428:
421:
413:
412:
411:
409:
405:
399:
392:
386:
363:
359:
355:
352:
349:
344:
340:
329:
321:
314:
306:
305:
304:
302:
298:
294:
289:
285:
276:
253:
250:
247:
239:
232:
222:
219:
216:
208:
201:
191:
188:
185:
177:
170:
160:
157:
154:
146:
139:
131:
130:
129:
123:
122:
121:
113:
111:
107:
103:
99:
95:
90:
88:
84:
83:sample median
80:
76:
71:
69:
65:
61:
57:
53:
49:
45:
41:
33:
29:
25:
21:
12708:Permutations
12674:
12662:
12643:
12636:
12548:Econometrics
12498: /
12481:Chemometrics
12458:Epidemiology
12451: /
12424:Applications
12266:ARIMA model
12213:Q-statistic
12162:Stationarity
12058:Multivariate
12001: /
11997: /
11995:Multivariate
11993: /
11933: /
11929: /
11703:Bayes factor
11602:Signed rank
11514:
11488:
11480:
11468:
11163:Completeness
11076:
10999:Cohort study
10897:Opinion poll
10832:Missing data
10819:Study design
10774:Scatter plot
10696:Scatter plot
10689:Spearman's Ï
10651:Grouped data
10344:
10291:
10285:
10250:
10246:
10236:
10227:
10217:February 26,
10215:. Retrieved
10201:
10195:
10182:
10165:
10161:
10155:
10136:
10130:
10117:
10091:
10085:
10075:
10071:
10069:
10060:(1): 70â81,
10057:
10053:
10047:
10027:
9997:
9990:
9963:
9957:
9932:
9923:
9904:
9774:
9770:
9762:
9757:
9755:
9144:
8877:is given by
8828:
8541:
8195:
8174:
8142:
8138:
7940:
7859:
7818:
7814:
7780:
7696:which holds
7218:
6972:
6672:
6663:delta method
6658:
6654:
6650:
6646:
6635:
6633:
6517:
6419:
6409:
6397:
6387:
6370:
6362:
6354:
6352:
6185:
6181:
6177:
6175:
6066:
6062:
6060:
6051:
5892:
5797:
5794:
5782:
4971:
4967:
4965:
4907:
4784:
4780:
4778:
4762:
4753:Alfréd Rényi
4747:
4743:
4741:
4608:
4604:
4598:
4593:
4589:
4581:
4517:
3541:
3355:
3351:
3349:
3197:
3193:
3191:
2990:
2986:
2982:
2978:
2974:
2933:
2680:
2675:
2669:
2664:
2656:
2652:
2650:
2640:
2636:
2634:
2631:
2373:
2369:
2365:
2322:
2318:
2314:
2310:
2306:
2302:
2298:
2294:
2259:
2173:
2171:
2020:is equal to
1986:
1719:
1696:
1683:
1372:
1160:
981:
943:
919:
901:
897:
890:
877:
873:
866:
859:
857:
851:
847:
840:
837:realizations
830:
815:
811:
804:
797:
795:
712:
708:
698:
653:
646:
642:
632:
629:
618:
497:sample range
494:
403:
397:
390:
387:
384:
296:
292:
290:
283:
274:
269:
127:
119:
91:
72:
55:
47:
43:
37:
27:
12676:WikiProject
12591:Cartography
12553:Jurimetrics
12505:Reliability
12236:Time domain
12215:(LjungâBox)
12137:Time-series
12015:Categorical
11999:Time-series
11991:Categorical
11926:(Bernoulli)
11761:Correlation
11741:Correlation
11537:JarqueâBera
11509:Chi-squared
11271:M-estimator
11224:Asymptotics
11168:Sufficiency
10935:Interaction
10847:Replication
10827:Effect size
10784:Violin plot
10764:Radar chart
10744:Forest plot
10734:Correlogram
10684:Kendall's Ï
10355:C++ source
9918:introducing
9823:L-estimator
8829:Similarly,
7919:within the
7344:jackknifing
6643:exponential
6390:sample mean
5799:median is
1810:. Denoting
907:independent
410:, that is,
124:6, 9, 3, 7,
92:When using
12692:Categories
12543:Demography
12261:ARMA model
12066:Regression
11643:(Friedman)
11604:(Wilcoxon)
11542:Normality
11532:Lilliefors
11479:Student's
11355:Resampling
11229:Robustness
11217:divergence
11207:Efficiency
11145:(monotone)
11140:Likelihood
11057:Population
10890:Stratified
10842:Population
10661:Dependence
10617:Count data
10548:Percentile
10525:Dispersion
10458:Arithmetic
10393:Statistics
10330:PlanetMath
9949:References
9901:references
9856:Percentile
4742:where the
922:continuous
85:and other
40:statistics
11924:Logistic
11691:posterior
11617:Rank sum
11365:Jackknife
11360:Bootstrap
11178:Bootstrap
11113:Parameter
11062:Statistic
10857:Statistic
10769:Run chart
10754:Pie chart
10749:Histogram
10739:Fan chart
10714:Bar chart
10596:L-moments
10483:Geometric
10346:MathWorld
10260:1412.2851
9709:−
9686:−
9631:−
9622:−
9614:−
9566:−
9525:−
9507:∑
9480:−
9420:−
9412:−
9328:−
9310:∑
9262:−
9253:≤
9118:−
9031:−
9013:∑
8982:−
8802:−
8723:−
8705:∑
8674:−
8606:≤
8512:−
8400:−
8230:…
8177:histogram
8158:^
8120:ℓ
8076:ℓ
8069:^
8054:ℓ
8012:ℓ
7978:∑
7969:ℓ
7956:ℓ
7905:ℓ
7875:ℓ
7837:→
7799:→
7790:ℓ
7764:^
7644:×
7559:−
7545:
7493:ℓ
7483:ℓ
7476:^
7431:∈
7395:ℓ
7385:ℓ
7317:−
7275:δ
7176:δ
7144:∫
6922:∗
6878:−
6873:∗
6844:∗
6771:∗
6763:−
6713:∗
6577:∑
6536:∑
6452:−
6392:, by the
6303:−
6275:−
6243:−
6224:∼
6216:⌉
6207:⌈
6141:−
6109:∼
6101:⌉
6092:⌈
6034:%
6028:≈
5875:%
5869:≈
5785:quantiles
5750:≤
5747:⋯
5744:≤
5731:≤
5675:⋯
5621:…
5581:…
5531:≤
5465:−
5435:−
5421:−
5415:−
5385:−
5355:−
5310:−
5292:−
5286:−
5268:−
5144:−
5114:−
5100:−
5055:−
5037:−
4708:−
4672:∑
4661:λ
4483:−
4474:−
4462:−
4453:
4447:∼
4367:−
4358:−
4343:−
4319:
4255:
4249:⋅
4243:−
4186:−
4114:−
4055:
4049:⋅
4043:−
4018:
3987:
3959:−
3937:
3860:−
3801:
3763:−
3754:−
3742:−
3733:
3727:∼
3708:−
3656:−
3617:≥
3605:≥
3566:−
3385:⋯
3307:…
3254:…
2907:−
2891:−
2877:−
2853:−
2847:−
2831:−
2825:−
2811:−
2787:−
2772:−
2612:−
2595:−
2589:−
2580:⋅
2571:⋅
2563:−
2540:−
2522:−
2235:−
2213:
2207:∼
2152:−
2138:−
2124:−
2101:−
2083:−
1887:…
1754:…
1640:−
1631:−
1616:≤
1596:…
1570:
1468:≤
1448:…
1422:
1350:−
1320:−
1306:−
1242:−
1224:−
1141:−
1111:−
1031:∑
885:they are
585:−
546:…
460:…
406:) is the
353:…
68:inference
12638:Category
12331:Survival
12208:Johansen
11931:Binomial
11886:Isotonic
11473:(normal)
11118:location
10925:Blocking
10880:Sampling
10759:QâQ plot
10724:Box plot
10706:Graphics
10601:Skewness
10591:Kurtosis
10563:Variance
10493:Heronian
10488:Harmonic
10277:14334678
10190:(1946).
10168:: 9â18.
10125:(1953).
9866:Quartile
9851:Quantile
9792:Box plot
9781:See also
8196:Suppose
7162:″
6402:kurtosis
4584:from an
3198:constant
2985:, 1 and
827:, ..., X
12664:Commons
12611:Kriging
12496:Process
12453:studies
12312:Wavelet
12145:General
11312:Plug-in
11106:L space
10885:Cluster
10586:Moments
10404:Outline
9914:improve
8139:end for
7941:end for
7817:6:
7666:matrix
7579:2: Set
7521:1: Set
6379:Bahadur
6365:is the
6357:is the
1701:on the
896:, ...,
881:form a
872:, ...,
846:, ...,
810:, ...,
408:maximum
301:minimum
100:from a
79:maximum
75:minimum
12533:Census
12123:Normal
12071:Manova
11891:Robust
11641:2-way
11633:1-way
11471:-test
11142:
10719:Biplot
10510:Median
10503:Lehmer
10445:Center
10306:
10275:
10106:
10035:
10005:
9978:
9903:, but
9871:Median
9861:Decile
9787:Rankit
8418:
8181:kernel
8143:return
7266:, and
7219:where
6518:where
6482:
6461:
6361:, and
6353:where
5713:where
5520:where
4436:where
2659:, the
2643:+ 1).
883:sample
394:, the
229:
226:
198:
195:
167:
164:
104:, the
42:, the
12157:Trend
11686:prior
11628:anova
11517:-test
11491:-test
11483:-test
11390:Power
11335:Pivot
11128:shape
11123:scale
10573:Shape
10553:Range
10498:Heinz
10473:Cubic
10409:Index
10273:S2CID
10255:arXiv
8137:11:
7542:round
6634:with
6416:Proof
1779:is a
1705:have
839:) of
50:of a
12390:Test
11590:Sign
11442:Wald
10515:Mode
10453:Mean
10304:ISBN
10219:2015
10104:ISBN
10033:ISBN
10003:ISBN
9976:ISBN
9876:Mean
9773:log
9750:and
9287:<
8914:<
8859:<
8497:>
8376:<
8284:and
8179:and
8141:12:
6653:and
4908:and
4763:The
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1419:Prob
749:and
704:even
495:The
295:(or
291:The
77:and
66:and
11570:BIC
11565:AIC
10328:at
10296:doi
10265:doi
10206:doi
10170:doi
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