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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 normalizing constant ： ウィキペディア英語版 normalizing constant The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics. ==Definition and examples== In probability theory, a normalizing constant is a constant by which an everywhere non-negative function must be multiplied so the area under its graph is 1, e.g., to make it a probability density function or a probability mass function.〔''Continuous Distributions'' at University of Alabama.〕〔Feller, 1968, p. 22.〕 For example, if we define :$p(x)=e^,\; x\backslash in(-\backslash infty,\backslash infty)$ we have :$\backslash int\_^\backslash infty\; p(x)\backslash ,dx=\backslash int\_^\backslash infty\; e^\backslash ,dx=\backslash sqrt,$ if we define a function $\backslash varphi(x)$ as :$\backslash varphi(x)=\; \backslash frac$ so that :$\backslash int\_^\backslash infty\; \backslash varphi(x)\backslash ,dx=\backslash int\_^\backslash infty\; \backslash frac\backslash ,dx=1$ then the function $\backslash varphi(x)$ is a probability density function.〔Feller, 1968, p. 174.〕 This is the density of the standard normal distribution. (''Standard'', in this case, means the expected value is 0 and the variance is 1.) And constant $\backslash frac^\backslash infty\; \backslash frac=e^\backslash lambda\; ,$ and consequently :$f(n)=\backslash frac$ is a probability mass function on the set of all nonnegative integers.〔Feller, 1968, p. 156.〕 This is the probability mass function of the Poisson distribution with expected value λ. Note that if the probability density function is a function of various parameters, so too will be its normalizing constant. The parametrised normalizing constant for the Boltzmann distribution plays a central role in statistical mechanics. In that context, the normalizing constant is called the partition function. 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「normalizing constant」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.