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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 Log-normal distribution ： ウィキペディア英語版 Log-normal distribution \ e^} | cdf = A log-normal process is the statistical realization of the multiplicative product of many independent random variables, each of which is positive. This is justified by considering the central limit theorem in the log domain. The log-normal distribution is the maximum entropy probability distribution for a random variate $X$ for which the mean and variance of $\backslash ln(X)$ are specified. ==Notation== Given a log-normally distributed random variable $X$ and two parameters $\backslash mu$ and $\backslash sigma$ that are, respectively, the mean and standard deviation of the variable’s natural logarithm, then the logarithm of $X$ is normally distributed, and we can write $X$ as :$X=e^$ with $Z$ a standard normal variable. This relationship is true regardless of the base of the logarithmic or exponential function. If $\backslash log\_a(Y)$ is normally distributed, then so is $\backslash log\_b(Y)$, for any two positive numbers $a,b\backslash neq\; 1$. Likewise, if $e^X$ is log-normally distributed, then so is $a^$, where $a$ is a positive number $\backslash neq\; 1$. On a logarithmic scale, $\backslash mu$ and $\backslash sigma$ can be called the ''location parameter'' and the ''scale parameter'', respectively. In contrast, the mean, standard deviation, and variance of the non-logarithmized sample values are respectively denoted $m$, ''s.d.'', and $v$ in this article. The two sets of parameters can be related as (see also Arithmetic moments below)〔("Lognormal mean and variance" )〕 :$$ \mu=\ln\left(\frac}}\right), \sigma=\sqrt\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「Log-normal 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.