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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 Discrete-stable distribution ： ウィキペディア英語版 Discrete-stable distribution The discrete-stable distributions are a class of probability distributions with the property that the sum of several random variables from such a distribution is distributed according to the same family. They are the discrete analogue of the continuous-stable distributions. The discrete-stable distributions have been used in numerous fields, in particular in scale-free networks such as the internet, social networks〔Barabási, Albert-László (2003). Linked: how everything is connected to everything else and what it means for business, science, and everyday life. New York, NY: Plum.〕 or even semantic networks Both classes of distribution have properties such as infinitely divisibility, power law tails and unimodality. The most well-known discrete stable distribution is the Poisson distribution which is a special case as the only discrete-stable distribution for which the mean and all higher-order moments are finite. == Definition == The discrete-stable distributions are defined through their probability-generating function :$G(s|\; \backslash nu,a)=\backslash sum\_^\backslash infty\; P(N|\; \backslash nu,a)(1-s)^N\; =\; \backslash exp(-a\; s^\backslash nu).$ In the above, $a>0$ is a scale parameter and describes the power-law behaviour such that when , :$\backslash lim\_P(N|\backslash nu,a)\; \backslash sim\; \backslash frac\backslash frac\backslash right|\_.$ A closed-form expression using elementary functions for the probability distribution of the discrete-stable distributions is not known except for in the Poisson case, in which :$\backslash !P(N|\; \backslash nu=1,\; a)=\; \backslash frac.$ Expressions do exist, however, using special functions for the case $\backslash nu=1/2$ (in terms of Bessel functions) and $\backslash nu=1/3$ (in terms of hypergeometric functions). 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「Discrete-stable 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.