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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 Yule–Simon distribution ： ウィキペディア英語版 Yule–Simon distribution \, for $\backslash rho>3$| kurtosis =$\backslash rho+3+\backslash frac$ for $\backslash rho>4$| entropy =| mgf =$\backslash frac$| }} In probability and statistics, the Yule–Simon distribution is a discrete probability distribution named after Udny Yule and Herbert A. Simon. Simon originally called it the ''Yule distribution''. The probability mass function (pmf) of the Yule–Simon (''ρ'') distribution is :$f(k;\backslash rho)\; =\; \backslash rho\backslash operatorname(k,\; \backslash rho+1)$, for integer $k\; \backslash geq\; 1$ and real $\backslash rho\; >\; 0$, where $\backslash operatorname$ is the beta function. Equivalently the pmf can be written in terms of the falling factorial as :$$ f(k;\rho) = \frac , where $\backslash Gamma$ is the gamma function. Thus, if $\backslash rho$ is an integer, :$$ f(k;\rho) = \frac . The parameter $\backslash rho$ can be estimated using a fixed point algorithm. The probability mass function ''f'' has the property that for sufficiently large ''k'' we have :$$ f(k;\rho) \approx \frac{k^{\rho+1}} . This means that the tail of the Yule–Simon distribution is a realization of Zipf's law: $f(k;\backslash rho)$ can be used to model, for example, the relative frequency of the $k$th most frequent word in a large collection of text, which according to Zipf's law is inversely proportional to a (typically small) power of $k$. ==Occurrence== The Yule–Simon distribution arose originally as the limiting distribution of a particular stochastic process studied by Yule as a model for the distribution of biological taxa and subtaxa.〔 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「Yule–Simon distribution」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.