β-分布的渐近抽样法及其在计算机上的实现

An Asymptotically Random Sampling Technique for Beta Distribution and Its Implement on Computer

迄今,在一般的随机模拟文献中,关于β分布的抽样主要讨论参数为正整数情形。本文借助于Polya罐子模型黑球比例数X_的极限分布为β—分布这一原理,提出了正有理参数β—分布的渐近抽样方法,给出了模拟算法,编制了程序。选取若干正有理数参数,在计算机上进行了随机模拟,产生了渐近于β—分布的随机数,并制成了随机数表。本文对其中一些样本应用各种统计方法进行了检验,结果表明,拟合性是非常好的。

In a series of articles about random simulation today,it is the main case to discuss positive integral parameters for ramdom sampling of Beta distribution. In this paper,based on the principle that the limit distribution of X, ,the fraction of black balls of Polya Urn at stage n ,has Beta distribution, we pose an asymptotically random sampling technique for Beta distribution with positive rational parameters. We give the simulated algorithm and program list. By selecting several different positive rational parameters,stochastic simulation is carried out on computer, asymptotically Beta distributial random numbers are generated .and random number tables are printed. By testing the sample by some statistical test methods,it is found that the goodness of fit is satisfactory.