On closeness of two discrete weighted sums

Vydas Čekanavičius; Palaniappan Vellaisamy

doi:10.15559/18-VMSTA103

paper

On closeness of two discrete weighted sums

arXiv:1806.03844 · doi:10.15559/18-VMSTA103

Abstract

The effect that weighted summands have on each other in approximations of $S = w_{1} S_{1} + w_{2} S_{2} + \dots + w_{N} S_{N}$ is investigated. Here, $S_{i}$ 's are sums of integer-valued random variables, and $w_{i}$ denote weights, $i = 1, \dots, N$ . Two cases are considered: the general case of independent random variables when their closeness is ensured by the matching of factorial moments and the case when the $S_{i}$ has the Markov Binomial distribution. The Kolmogorov metric is used to estimate the accuracy of approximation.

Published at https://doi.org/10.15559/18-VMSTA103 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)