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arXiv · 1806.03844

On closeness of two discrete weighted sums

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.

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Vydas Čekanavičius, Palaniappan Vellaisamy. 2018-06-11. On closeness of two discrete weighted sums. https://doi.org/10.15559/18-vmsta103

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