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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 Exponential dispersion model ： ウィキペディア英語版 Exponential dispersion model Exponential dispersion models are statistical models in which the probability distribution is of a special form.〔Marriott, P. (2005) "Local Mixtures and Exponential Dispersion Models" (pdf )〕〔Jørgensen, B. (1987). Exponential dispersion models (with discussion). Journal of the Royal Statistical Society, Series B, 49 (2), 127–162.〕 This class of models represents a generalisation of the exponential family of models which themselves play an important role in statistical theory because they have a special structure which enables deductions to be made about appropriate statistical inference. ==Definition== Exponential dispersion models are a generalisation of the natural exponential family: these have a probability density function which, for a multivariate model, can be written as :$f\_X(\backslash mathbf|\backslash boldsymbol)\; =\; h(\backslash mathbf)\; \backslash exp(\backslash boldsymbol\backslash theta^\backslash top\; \backslash mathbf\; -\; A(\backslash boldsymbol\backslash theta))\; \backslash ,\backslash !\; ,$ where the parameter $\backslash boldsymbol\backslash theta$ has the same dimension as the observation variable $\backslash mathbf$. The generalisation includes an extra scalar "index parameter", $\backslash lambda$, and has density function of the form〔 :$f\_X(\backslash mathbf|\backslash lambda,\backslash boldsymbol)\; =\; h(\backslash lambda,\backslash mathbf)\; \backslash exp\; (\backslash lambda\; (\backslash mathbf\; -\; A(\backslash boldsymbol\backslash theta))\; )\; \backslash ,\backslash !\; .$ The terminology "dispersion parameter" is used for $\backslash sigma^2=\backslash lambda^$, while $\backslash boldsymbol\backslash theta$ is the "natural parameter" (also known as "canonical parameter"). 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「Exponential dispersion model」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.