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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 Generalized integer gamma distribution ： ウィキペディア英語版 Generalized integer gamma distribution In probability and statistics, the generalized integer gamma distribution (GIG) is the distribution of the sum of independent gamma distributed random variables, all with integer shape parameters and different rate parameters. This is a special case of the generalized chi-squared distribution. A related concept is the generalized near-integer gamma distribution (GNIG). ==Definition== The random variable $X\backslash !$ has a gamma distribution with shape parameter $r$ and rate parameter $\backslash lambda$ if its probability density function is :$$ f^\,e^ x^~~~~~~(x>0;\,\lambda,r>0) and this fact is denoted by $X\backslash sim\backslash Gamma(r,\backslash lambda)\backslash !.$ Let $X\_j\backslash sim\backslash Gamma(r\_j,\backslash lambda\_j)\backslash !$, where $(j=1,\backslash dots,p),$ be $p$ independent random variables, with all $r\_j$ being positive integers and all $\backslash lambda\_j\backslash !$ different. In other words, each variable has the Erlang distribution with different shape parameters. The uniqueness of each shape parameter comes without loss of generality, because any case where some of the $\backslash lambda\_j$ are equal would be treated by first adding the corresponding variables: this sum would have a gamma distribution with the same rate parameter and a shape parameter which is equal to the sum of the shape parameters in the original distributions. Then the random variable ''Y'' defined by :$$ Y=\sum^p_ X_j has a GIG (generalized integer gamma) distribution of depth $p$ with shape parameters $r\_j\backslash !$ and rate parameters $\backslash lambda\_j\backslash !$ $(j=1,\backslash dots,p)$. This fact is denoted by :$Y\backslash sim\; GIG(r\_j,\backslash lambda\_j;p)\backslash !\; .$ It is also a special case of the generalized chi-squared distribution. 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「Generalized integer gamma 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.