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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 Exponentially modified Gaussian distribution ： ウィキペディア英語版 Exponentially modified Gaussian distribution \right)-\frac $f(x\_m)=h\backslash exp\; \backslash left(\; -\backslash frac\; \backslash left(\; \backslash frac\; \backslash right)^2\backslash right)$| variance =$\backslash sigma^2\; +\; 1/\backslash lambda^2$| skewness =$\backslash frac\; \backslash left(\; 1\; +\; \backslash frac\; \backslash right)^$| kurtosis =$\backslash frac\; +\; \backslash frac)\}\; \backslash right)^2\; \}\; -\; 3$| entropy =| mgf = $\backslash left(1\; -\; \backslash frac\backslash right)^\backslash ,\backslash exp\; \backslash \backslash sigma^2\; t^2\; \backslash \}$| cf = $\backslash left(1\; -\; \backslash frac\backslash right)^\backslash ,\backslash exp\; \backslash \backslash sigma^2\; t^2\; \backslash \}$| }} In probability theory, an exponentially modified Gaussian (EMG) distribution (ExGaussian distribution) describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = ''X'' + ''Y'' where ''X'' and ''Y'' are independent, ''X'' is Gaussian with mean ''μ'' and variance ''σ''2 and ''Y'' is exponential of rate ''λ''. It has a characteristic positive skew from the exponential component. It may also be regarded as a weighted function of a shifted exponential with the weight being a function of the normal distribution. ==Definition== The probability density function (pdf) of the exponentially modified normal distribution is :$f(x;\backslash mu,\backslash sigma,\backslash lambda)\; =\; \backslash frac\; e^\; (2\; \backslash mu\; +\; \backslash lambda\; \backslash sigma^2\; -\; 2\; x)\}$ \operatorname \left(\frac\right) where erfc is the complementary error function defined as :$\backslash begin$ \operatorname(x) & = 1-\operatorname(x) \\ & = \frac\,dt. \end This density function is derived via convolution of the normal and exponential probability density functions. The density function is a solution of the following differential equation: : $$ \left\ \sigma ^2 f''(x)+f'(x) \left(\lambda \sigma ^2-\mu +x\right)+\lambda f(x) (x-\mu)=0, \\() f(0)=\frac \lambda e^ \lambda \left(\lambda \sigma ^2+2 \mu \right)} \text\left(\frac\right), \\() f'(0)=\frac} \left(\sqrt-\sqrt \lambda \sigma e^} \text\left(\frac\right)\right)} \end \right\} 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「Exponentially modified Gaussian 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.