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On closeness of two discrete weighted sums
Volume 5, Issue 2 (2018), pp. 207–224
Vydas Čekanavičius   Palaniappan Vellaisamy  

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https://doi.org/10.15559/18-VMSTA103
Pub. online: 21 May 2018      Type: Research Article      Open accessOpen Access

Received
1 February 2018
Revised
16 April 2018
Accepted
27 April 2018
Published
21 May 2018

Abstract

The effect that weighted summands have on each other in approximations of $S={w_{1}}{S_{1}}+{w_{2}}{S_{2}}+\cdots +{w_{N}}{S_{N}}$ 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.

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Keywords
Characteristic function concentration function factorial moments Kolmogorov metric Markov Binomial distribution weighted random variables

MSC2010
60F05 60J10

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