Departmental Bulletin Paper 正規分布の裾の確率評価と乱数生成

中村, 永友  ,  土屋, 高宏

 コンピュータ上で何らかの数値実験やシミュレーションを行う際に,正規乱数を使う場面が多くある.多くの場合,正規乱数を直接求めるのではなく,一様乱数から何らかの変換を通して得ている.本報告では,超大量の正規分布の裾の乱数,具体的には5σ以上,を得るための方法を提案する.目的の連続型確率分布の乱数は,離散型確率分布の近似を通して生成する.近似した確率分布であるオイラリアン分布の正規分布に対する裾の確率近似の良さを示し,同時に乱数生成アルゴリズムを提示する. The random numbers that follow a normal distribution, the normal random numbers, are used in numerical experiments or simulation studies in several experimental sciences. The normal random numbers do not directly generate it, but these obtain uniform random numbers through some transformations. In this report, we propose a method to generate random numbers at the tail of a very large amount of normal distribution, specifically 5σ or more. The random number of a continuous probability distribution target is generated through an approximation to a discrete probability distribution. The approximate probability distribution, the Eulerian distribution, also shows the merits of the probability approximation of the tail to the normal distribution. At the same time, we present a random number generation algorithm.

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