An acceptance-rejection algorithm for the kolmogorov distribution

Abstract

We discuss an acceptance-rejection algorithm for the random number generation from the Kolmogorov distribution. Since the cumulative distribution function (CDF) is a functions series and we need the density distribution function in our algorithm, we prove that the series of the derivatives converges uniformly in order to can derive term by term the functions series; also we provide
a similar proof for showing that the ratio between the target Kolmogorov density and the auxiliary density implemented is bounded. Finally, for the application in the algorithm we propose to approximate the density of Kolmogorov distribution by truncation series where the truncation is posed as far away as possible according to the precision of the calculator, we asses the accuracy of this method by a simulation study.