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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 Gaussian q-distribution ： ウィキペディア英語版 Gaussian q-distribution In mathematical physics and probability and statistics, the Gaussian ''q''-distribution is a family of probability distributions that includes, as limiting cases, the uniform distribution and the normal (Gaussian) distribution. It was introduced by Diaz and Teruel, is a q-analogue of the Gaussian or normal distribution. The distribution is symmetric about zero and is bounded, except for the limiting case of the normal distribution. The limiting uniform distribution is on the range -1 to +1. ==Definition== Let ''q'' be a real number in the interval ''q'' of the real number $t$ is given by : $()\_q=\backslash frac.$ The ''q''-analogue of the exponential function is the q-exponential, ''E'', which is given by : $E\_q^=\backslash sum\_^q^\backslash frac$ where the ''q''-analogue of the factorial is the q-factorial, ()''q''!, which is in turn given by : $()\_q!=()\_q()\_q\backslash cdots\; ()\_q\; \backslash ,$ for an integer ''n'' > 2 and ()''q''! = ()''q''! = 1. The cumulative distribution function of the Gaussian ''q''-distribution is given by : \displaystyle \frac\int_^ E_^ \, d_qt & \text -\nu \leq x \leq \nu \\() 1 & \text x>\nu \end where the integration symbol denotes the Jackson integral. The function ''G''''q'' is given explicitly by : \displaystyle \frac + \frac \sum_^\infty \frac^}x^ & \text -\nu \leq x \leq \nu \\ 1 & \text\ x > \nu \end where : $(a+b)\_q^n=\backslash prod\_^(a+q^ib)\; .$ 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「Gaussian q-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.