On the rate of convergence of the distributions of certain statistics to the Laplace and student distributions

Abstract

This work deals with asymptotically normal statistics. If the size of sample is replaced by a random variable that is the maximum of n independent random variables with Pareto discrete distribution, then the distribution of these statistics is asymptotically Laplacian. If the size of the sample is replaced by a random variable with negative binomial distribution, then the distribution of these statistics is asymptotically a Student distribution. In the present study, the rates of convergences of these statistics’ distributions to the corresponding limiting distributions are estimated and the constants from expressions for estimating the rates are determined more accurately.