On closeness of two discrete weighted sums

Vydas Čekanavičius; Palaniappan Vellaisamy

doi:10.15559/18-VMSTA103

On closeness of two discrete weighted sums

Probability 2018-06-12 v1

Authors: Vydas Čekanavičius , Palaniappan Vellaisamy

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Abstract

The effect that weighted summands have on each other in approximations of $S=w_1S_1+w_2S_2+\cdots+w_NS_N$ 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.

Keywords

discrete weighted sums factorial moments Markov Binomial distribution Kolmogorov metric integer-valued random variables

Cite

@article{arxiv.1806.03844,
  title  = {On closeness of two discrete weighted sums},
  author = {Vydas Čekanavičius and Palaniappan Vellaisamy},
  journal= {arXiv preprint arXiv:1806.03844},
  year   = {2018}
}

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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/)

On closeness of two discrete weighted sums

Abstract

Keywords

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