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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 Poisson binomial distribution ： ウィキペディア英語版 Poisson binomial distribution In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. The concept is named after Siméon Denis Poisson. In other words, it is the probability distribution of the number of successes in a sequence of ''n'' independent yes/no experiments with success probabilities $p\_1,\; p\_2,\; \backslash dots\; ,\; p\_n$. The ordinary binomial distribution is a special case of the Poisson binomial distribution, when all success probabilities are the same, that is $p\_1\; =\; p\_2\; =\; \backslash cdots\; =\; p\_n$. ==Mean and variance== Since a Poisson binomial distributed variable is a sum of ''n'' independent Bernoulli distributed variables, its mean and variance will simply be sums of the mean and variance of the ''n'' Bernoulli distributions: : $\backslash mu\; =\; \backslash sum\backslash limits\_^n\; p\_i$ : $\backslash sigma^2\; =\backslash sum\backslash limits\_^n\; (1-p\_i)\; p\_i$ For fixed values of the mean ($\backslash mu$) and size (''n''), the variance is maximal when all success probabilities are equal and we have a binomial distribution. When the mean is fixed, the variance is bounded from above by the variance of the Poisson distribution with the same mean which is attained asymptotically as ''n'' tends to infinity. 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「Poisson binomial 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.