We discuss an acceptance-rejection algorithm for the random number generation from the Kolmogorov distribution. Since the cumulative distribution function (CDF) is expressed as a series, in order to obtain the density function we need to prove that the series of the derivatives converges uniformly. We also provide a similar proof in order to show that the ratio between the target Kolmogorov density and the auxiliary density implemented is bounded. Finally we discuss a way of truncating the series expression of the density in an optimal way.
翻译:我们讨论从 Kolmogorov 分布的随机数字生成的接受-拒绝算法。 由于累积分布函数(CDF) 是一个序列表达, 为了获得密度函数, 我们需要证明衍生物序列一致。 我们还提供了类似的证明, 以显示目标 Kolmogorov 密度与执行的辅助密度之间的比例是捆绑的。 最后我们讨论如何以最佳方式缩短密度序列表达方式 。