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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Concomitant (statistics) ： ウィキペディア英語版 Concomitant (statistics) In statistics, the concept of a concomitant, also called the induced order statistic, arises when one sorts the members of a random sample according to corresponding values of another random sample. Let (''X''''i'', ''Y''''i''), ''i'' = 1, . . ., ''n'' be a random sample from a bivariate distribution. If the sample is ordered by the ''X''''i'', then the ''Y''-variate associated with ''X''''r'':''n'' will be denoted by ''Y''() and termed the concomitant of the ''r''th order statistic. Suppose the parent bivariate distribution having the cumulative distribution function ''F(x,y)'' and its probability density function ''f(x,y)'', then the probability density function of ''r''''th'' concomitant $Y\_$ for $1\; \backslash le\; r\; \backslash le\; n$ is $f\_^\backslash infty\; f\_(y|x)\; f\_\; x$ If all $(X\_i,\; Y\_i)$ are assumed to be i.i.d., then for , the joint density for $\backslash left(Y\_,\; \backslash cdots,\; Y\_\; \backslash right)$ is given by $f\_\; \}(y\_1,\; \backslash cdots,\; y\_k)\; =\; \backslash int\_^\backslash infty\; \backslash int\_^\; \backslash cdots\; \backslash int\_^\; \backslash prod^k\_\; f\_\; (y\_i|x\_i)\; f\_\}(x\_1,\backslash cdots,x\_k)\backslash mathrmx\_1\backslash cdots\; \backslash mathrmx\_k$ That is, in general, the joint concomitants of order statistics $\backslash left(Y\_,\; \backslash cdots,\; Y\_\; \backslash right)$ is dependent, but are conditionally independent given $X\_\; =\; x\_1,\; \backslash cdots,\; X\_\; =\; x\_k$ for all ''k'' where $x\_1\; \backslash le\; \backslash cdots\; \backslash le\; x\_k$. The conditional distribution of the joint concomitants can be derived from the above result by comparing the formula in marginal distribution and hence $f\_\; \backslash mid\; X\_\; \backslash cdots\; X\_\; \}(y\_1,\; \backslash cdots,\; y\_k\; |\; x\_1,\; \backslash cdots,\; x\_k)\; =\; \backslash prod^k\_\; f\_\; (y\_i|x\_i)$ ==References== * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Concomitant (statistics)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.