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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 Neutral vector ： ウィキペディア英語版 Neutral vector In statistics, and specifically in the study of the Dirichlet distribution, a neutral vector of random variables is one that exhibits a particular type of statistical independence amongst its elements.〔 〕 In particular, when elements of the random vector must add up to certain sum, then an element in the vector is neutral with respect to the others if the distribution of the vector created by expressing the remaining elements as proportions of their total is independent of the element that was omitted. ==Definition== A single element $X\_i$ of a random vector $X\_1,X\_2,\backslash ldots,X\_k$ is neutral if the ''relative'' proportions of all the other elements are independent of $X\_i$. The concept was originally developed for the study of turtle scutes. Formally, consider the vector of random variables :$X=X\_1,\backslash ldots,X\_k$ where :$\backslash sum\_^k\; X\_i=1.$. The values $X\_i$ are interpreted as lengths whose sum is unity. In a variety of contexts, it is often desirable to eliminate a proportion, say $X\_1$, and consider the distribution of the remaining intervals within the remaining length. The first element of $X$, viz $X\_1$ is defined as ''neutral'' if $X\_1$ is statistically independent of the vector :$X^$ *_1=X_2/(1-X_1),X_3/(1-X_1),\ldots,X_k/(1-X_1). Variable $X\_2$ is neutral if $X\_2/(1-X\_1)$ is independent of the remaining interval: that is, $X\_2/(1-X\_1)$ being independent of :$X^$ *_=X_3/(1-X_1-X_2),X_4/(1-X_1-X_2),\ldots,X_k/(1-X_1-X_2). Thus $X\_2$, viewed as the first element of $Y=X\_2,X\_3,\backslash ldots,X\_k$, is neutral. In general, variable $X\_j$ is neutral if $X\_1,\backslash ldots\; X\_$ is independent of :$X^$ *_=X_/(1-X_1-\cdots -X_j),\ldots X_k/(1-X_1-\cdots - X_j). A vector for which each element is neutral is completely neutral. If $X\; =\; (X\_1,\; \backslash ldots,\; X\_K)\backslash sim\backslash operatorname(\backslash alpha)$ is drawn from a Dirichlet distribution, then $X$ is completely neutral. In 1980, James and Mosimann showed that the Dirichlet distribution is characterised by neutrality. 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「Neutral vector」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.