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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 Normal-gamma distribution ： ウィキペディア英語版 Normal-gamma distribution }\,e^\,e^}| cdf =| mean =〔Bernardo & Smith (1993, p.434)〕 $\backslash operatorname(X)=\backslash mu\backslash ,\backslash !\; ,\backslash quad\; \backslash operatorname(\backslash Tau)=\; \backslash alpha\; \backslash beta^$ | median = | mode = $\backslash left(\backslash mu,\; \backslash frac\backslash right)$| variance =〔 $\backslash operatorname(X)=\; \backslash frac\; ,\backslash quad$ \operatorname(\Tau)=\alpha \beta^ | skewness =| kurtosis =| entropy =| mgf =| char =| }} In probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and precision.〔Bernardo & Smith (1993, pages 136, 268, 434)〕 ==Definition== For a pair of random variables, (''X'',''T''), suppose that the conditional distribution of ''X'' given ''T'' is given by :$X|T\; \backslash sim\; N(\backslash mu,1\; /(\backslash lambda\; T))\; \backslash ,\backslash !\; ,$ meaning that the conditional distribution is a normal distribution with mean $\backslash mu$ and precision $\backslash lambda\; T$ — equivalently, with variance $1\; /\; (\backslash lambda\; T)\; .$ Suppose also that the marginal distribution of ''T'' is given by :$T\; |\backslash alpha,\; \backslash beta\; \backslash sim\; \backslash mathrm(\backslash alpha,\backslash beta)\; \backslash !\; ,$ where this means that ''T'' has a gamma distribution. Here λ, α and β are parameters of the joint distribution. Then (''X'',''T'') has a normal-gamma distribution, and this is denoted by :$(X,T)\; \backslash sim\; \backslash mathrm(\backslash mu,\backslash lambda,\backslash alpha,\backslash beta)\; \backslash !\; .$ 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「Normal-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.