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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 Smoothness (probability theory) ： ウィキペディア英語版 Smoothness (probability theory) In probability theory and statistics, smoothness of a density function is a measure which determines how many times the density function can be differentiated, or equivalently the limiting behavior of distribution’s characteristic function. Formally, we call the distribution of a random variable ''X'' ordinary smooth of order ''β'' if its characteristic function satisfies : $d\_0\; |t|^\; \backslash leq\; \backslash varphi\_X(t)\; \backslash leq\; d\_1\; |t|^\; \backslash quad\; \backslash text\; t\backslash to\backslash infty$ for some positive constants ''d''0, ''d''1, ''β''. The examples of such distributions are gamma, exponential, uniform, etc. The distribution is called supersmooth of order ''β'' 〔 if its characteristic function satisfies : $d\_0\; |t|^\backslash exp\backslash big(-|t|^\backslash beta/\backslash gamma\backslash big)\; \backslash leq\; \backslash varphi\_X(t)\; \backslash leq\; d\_1\; |t|^\backslash exp\backslash big(-|t|^\backslash beta/\backslash gamma\backslash big)\; \backslash quad\; \backslash text\; t\backslash to\backslash infty$ for some positive constants ''d''0, ''d''1, ''β'', ''γ'' and constants ''β''0, ''β''1. Such supersmooth distributions have derivatives of all orders. Examples: normal, Cauchy, mixture normal. == References == * 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「Smoothness (probability theory)」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.