Upper-bound estimates for weighted sums satisfying Cramer’s condition
Articles
Vydas Čekanavičius
Vilnius University
Aistė Elijio
Vilnius University
Published 2023-09-21
https://doi.org/10.15388/LMR.2006.30784
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Keywords

compound Poisson distribution
signed compound Poissonmeasure
Kolmogorov distance

How to Cite

Čekanavičius, V. and Elijio, A. (2023) “Upper-bound estimates for weighted sums satisfying Cramer’s condition”, Lietuvos matematikos rinkinys, 46(spec.), pp. 427–432. doi:10.15388/LMR.2006.30784.

Abstract

Let S = ω1S1 + ω2S2 + ⋯ + ωNSN. Here Sj is the sum of identically distributed random variables and ω > 0 denotes weight. We consider the case, when Sis the sum of independent random variables satisfying Cramer’s condition. Upper-bounds for the accuracy of compound Poisson first and second order approximations in uniformmetric are established.

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