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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 variance-mean mixture ： ウィキペディア英語版 Normal variance-mean mixture In probability theory and statistics, a normal variance-mean mixture with mixing probability density $g$ is the continuous probability distribution of a random variable $Y$ of the form :$Y=\backslash alpha\; +\; \backslash beta\; V+\backslash sigma\; \backslash sqrtX,$ where $\backslash alpha$, $\backslash beta$ and $\backslash sigma\; >\; 0$ are real numbers, and random variables $X$ and $V$ are independent, $X$ is normally distributed with mean zero and variance one, and $V$ is continuously distributed on the positive half-axis with probability density function $g$. The conditional distribution of $Y$ given $V$ is thus a normal distribution with mean $\backslash alpha\; +\; \backslash beta\; V$ and variance $\backslash sigma^2\; V$. A normal variance-mean mixture can be thought of as the distribution of a certain quantity in an inhomogeneous population consisting of many different normal distributed subpopulations. It is the distribution of the position of a Wiener process (Brownian motion) with drift $\backslash beta$ and infinitesimal variance $\backslash sigma^2$ observed at a random time point independent of the Wiener process and with probability density function $g$. An important example of normal variance-mean mixtures is the generalised hyperbolic distribution in which the mixing distribution is the generalized inverse Gaussian distribution. The probability density function of a normal variance-mean mixture with mixing probability density $g$ is :$f(x)\; =\; \backslash int\_0^\backslash infty\; \backslash frac\; \backslash right)\; g(v)\; \backslash ,\; dv$ and its moment generating function is :$M(s)\; =\; \backslash exp(\backslash alpha\; s)\; \backslash ,\; M\_g\; \backslash left(\backslash beta\; s\; +\; \backslash frac12\; \backslash sigma^2\; s^2\; \backslash right),$ where $M\_g$ is the moment generating function of the probability distribution with density function $g$, i.e. :$M\_g(s)\; =\; E\backslash left(\backslash exp(\; s\; V)\backslash right)\; =\; \backslash int\_0^\backslash infty\; \backslash exp(s\; v)\; g(v)\; \backslash ,\; dv.$ ==See also== : *Normal-inverse Gaussian 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「Normal variance-mean mixture」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.