Bounds for convergence rate in laws of large numbers for mixed Poisson random sums
Victor Korolev and
Alexander Zeifman
Statistics & Probability Letters, 2021, vol. 168, issue C
Abstract:
In the paper, upper bounds for the rate of convergence in laws of large numbers for mixed Poisson random sums are constructed. As a measure of the distance between the limit and pre-limit laws, the Zolotarev ζ-metric is used. The obtained results extend the known convergence rate estimates for geometric random sums (in the famous Rényi theorem) to a considerably wider class of random indices with mixed Poisson distributions including, e.g., those with the (generalized) negative binomial distribution.
Keywords: Law of large numbers; Convergence rate; Zolotarev ζ-metric; Poisson random sum; Mixed Poisson distribution; Geometric random sum (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:168:y:2021:i:c:s0167715220302212
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DOI: 10.1016/j.spl.2020.108918
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