翻訳と辞書 Words near each other ・ Boxwood Lodge ・ Boxwood Plantation Slave Quarter ・ Boxwood Public School ・ Boxwork ・ Boxworth ・ BOXX Technologies ・ Boxxle ・ Boxxy ・ Boxy ・ Boxy an Star ・ Boxy Boy ・ Box–Behnken design ・ Box–Cox distribution ・ Box–ironbark forest ・ Box–Jenkins ・ Box–Muller transform ・ Boy ・ Boy & a Girl Thing ・ Boy & Bear ・ Boy & Girl ・ Boy & Girl Band Indonesia ・ Boy & Kris ・ Boy & the World ・ Boy (1969 film) ・ Boy (2009 film) ・ Boy (2010 film) ・ Boy (album) ・ Boy (Book of Love song) ・ Boy (book) ・ Boy (Canadian band) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Box–Muller transform ： ウィキペディア英語版 Box–Muller transform The Box–Muller transform, by George Edward Pelham Box and Mervin Edgar Muller 1958,〔(G. E. P. Box and Mervin E. Muller, ''A Note on the Generation of Random Normal Deviates'', The Annals of Mathematical Statistics (1958), Vol. 29, No. 2 pp. 610–611 )〕 is a pseudo-random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation, unit variance) random numbers, given a source of uniformly distributed random numbers. It is commonly expressed in two forms. The basic form as given by Box and Muller takes two samples from the uniform distribution on the interval (0, 1] and maps them to two standard, normally distributed samples. The polar form takes two samples from a different interval, (), and maps them to two normally distributed samples without the use of sine or cosine functions. The Box–Muller transform was developed as a more computationally efficient alternative to the inverse transform sampling method.〔Kloeden and Platen, ''Numerical Solutions of Stochastic Differential Equations'', pp. 11–12〕 The Ziggurat algorithm gives an even more efficient method. Furthermore, the Box–Muller transform can be also employed from drawing from truncated bivariate Gaussian densities. == Basic form == Suppose ''U''1 and ''U''2 are independent random variables that are uniformly distributed in the interval (0, 1). Let :$Z\_0\; =\; R\; \backslash cos(\backslash Theta)\; =\backslash sqrt\; \backslash cos(2\; \backslash pi\; U\_2)\backslash ,$ and :$Z\_1\; =\; R\; \backslash sin(\backslash Theta)\; =\; \backslash sqrt\; \backslash sin(2\; \backslash pi\; U\_2).\backslash ,$ Then ''Z''0 and ''Z''1 are independent random variables with a standard normal distribution. The derivation〔Sheldon Ross, ''A First Course in Probability'', (2002), pp. 279–281〕 is based on a property of a two-dimensional Cartesian system, where X and Y coordinates are described by two independent and normally distributed random variables, the random variables for ''R''2 and Θ (shown above) in the corresponding polar coordinates are also independent and can be expressed as :$R^2\; =\; -2\backslash cdot\backslash ln\; U\_1\backslash ,$ and :$\backslash Theta\; =\; 2\backslash pi\; U\_2.\; \backslash ,$ Because ''R''2 is the square of the norm of the standard bivariate normal variable (X, Y), it has the chi-squared distribution with two degrees of freedom. In the special case of two degrees of freedom, the chi-squared distribution coincides with the exponential distribution, and the equation for ''R''2 above is a simple way of generating the required exponential variate. 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「Box–Muller transform」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.