On closeness of two discrete weighted sums
Volume 5, Issue 2 (2018), pp. 207–224
Pub. online: 21 May 2018
Type: Research Article
Open Access
Open Access
Received
1 February 2018
1 February 2018
Revised
16 April 2018
16 April 2018
Accepted
27 April 2018
27 April 2018
Published
21 May 2018
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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