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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 Marsaglia polar method ： ウィキペディア英語版 Marsaglia polar method The polar method (attributed to George Marsaglia, 1964〔(A convenient method for generating normal variables, G. Marsaglia and T. A. Bray, SIAM Rev. 6, 260–264, 1964 )〕) is a pseudo-random number sampling method for generating a pair of independent standard normal random variables.〔Peter E. Kloeden Eckhard Platen Henri Schurz, Numerical Solution of SDE Through Computer Experiments, Springer, 1994.〕 While it is superior to the Box–Muller transform,〔.〕 the Ziggurat algorithm is even more efficient.〔D. Thomas and W. Luk and P. Leong and J. Villasenor (2007), (Gaussian Random Number Generators ), ''ACM Computing Surveys'', Vol. 39(4), Article 11, 〕 Standard normal random variables are frequently used in computer science, computational statistics, and in particular, in applications of the Monte Carlo method. The polar method works by choosing random points (''x'', ''y'') in the square −1 < ''x'' < 1, −1 < ''y'' < 1 until : and then returning the required pair of normal random variables as :$x\backslash sqrt\}\backslash ,,\backslash \; \backslash \; y\backslash sqrt\}.$ ==Theoretical basis== The underlying theory may be summarized as follows: If ''u'' is uniformly distributed in the interval 0 ≤ ''u'' < 1, then the point (cos(2π''u''), sin(2π''u'')) is uniformly distributed on the unit circumference ''x''2 + ''y''2 = 1, and multiplying that point by an independent random variable ρ whose distribution is : will produce a point :$\backslash left(\backslash rho\backslash cos(2\backslash pi\; u),\backslash rho\backslash sin(2\backslash pi\; u)\backslash right)$ whose coordinates are jointly distributed as two independent standard normal random variables. 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「Marsaglia polar method」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.