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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 Chernoff's distribution ： ウィキペディア英語版 Chernoff's distribution In probability theory, Chernoff's distribution, named after Herman Chernoff, is the probability distribution of the random variable : $Z\; =\backslash underset\}\backslash \; (W(s)\; -\; s^2),$ where ''W'' is a "two-sided" Wiener process (or two-sided "Brownian motion") satisfying ''W''(0) = 0. If : $V(a,c)\; =\; \backslash underset\}\; \backslash \; (W(s)\; -\; c(s-a)^2),$ then ''V''(0, ''c'') has density : $f\_c(t)\; =\; \backslash frac\; g\_c(t)\; g\_c(-t)$ where ''g''''c'' has Fourier transform given by : $\backslash hat\_c\; (s)\; =\; \backslash frac\; (i\; (2c^2)^\; s)\},\; \backslash \; \backslash \; \backslash \; s\; \backslash in\; \backslash mathbf$ and where Ai is the Airy function. Thus ''f''''c'' is symmetric about 0 and the density ''ƒ''''Z'' = ''ƒ''1. Groeneboom (1989) shows that :$f\_Z\; (z)\; \backslash sim\; \backslash frac\; \backslash frac\_1)\}\; \backslash exp\; \backslash left(\; -\; \backslash frac\; |z|^3\; +\; 2^\; \backslash tilde\_1\; |z|\; \backslash right)$ \textz \rightarrow \infty where $\backslash tilde\_1\; \backslash approx\; -2.3381$ is the largest zero of the Airy function Ai and where $\backslash operatorname\text{'}\; (\backslash tilde\_1\; )\; \backslash approx\; 0.7022$. == References == * * * Piet Groeneboom (1985). Estimating a monotone density. In: Le Cam, L.E., Olshen, R. A. (eds.), Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer, vol. II, pp. 539–555. Wadsworth. 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「Chernoff's 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.