An Efficient Randomized Quasi-Monte Carlo Algorithm for the Pareto Distribution

摘要

This paper studies a new randomized quasi-Monte Carlo method for estimating the mean and variance of the Pareto distribution. In many Monte Carlo simulations, there are some stability problems for estimating the population Pareto variance by using the sample variance. In this paper, we propose a randomized quasi-random number generator [quasi-RNG] to generate Pareto random samples, such that the sample mean and sample variance estimators gain more efficiency. The efficiency of this generator relative to the popular linear congruential random number generator [LC-RNG] is studied by using the simulation mean square errors. We also compare the results of the Kolmogorov-Smirnov goodness-of-fit tests using these two sample generators.