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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 Gauss–Kuzmin distribution ： ウィキペディア英語版 Gauss–Kuzmin distribution In mathematics, the Gauss–Kuzmin distribution is a discrete probability distribution that arises as the limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1). The distribution is named after Carl Friedrich Gauss, who derived it around 1800, and Rodion Kuzmin, who gave a bound on the rate of convergence in 1929. It is given by the probability mass function : $p(k)\; =\; -\; \backslash log\_2\; \backslash left(\; 1\; -\; \backslash frac\backslash right)~.$ ==Gauss–Kuzmin theorem== Let :$x\; =\; \backslash frac\}$ be the continued fraction expansion of a random number ''x'' uniformly distributed in (0, 1). Then :$\backslash lim\_\; \backslash mathbb\; \backslash left\backslash \; =\; -\; \backslash log\_2\backslash left(1\; -\; \backslash frac\backslash right)~.$ Equivalently, let :$x\_n\; =\; \backslash frac\}~;$ then :$\backslash Delta\_n(s)\; =\; \backslash mathbb\; \backslash left\backslash \; -\; \backslash log\_2(1+s)$ tends to zero as ''n'' tends to infinity. 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「Gauss–Kuzmin 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.