Some estimates of the normal approximation for mixture of Poisson and gamma random variables
Articles
Jonas Kazys Sunklodas
Institute of Mathematics and Informatics
Published 2010-12-21
https://doi.org/10.15388/LMR.2010.86
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Keywords

normal approximation
Lp norms
Poisson distribution
gamma distribution
mixture of Poisson and gamma r.v.

How to Cite

Sunklodas J. K. (2010) “Some estimates of the normal approximation for mixture of Poisson and gamma random variables”, Lietuvos matematikos rinkinys, 51(proc. LMS), pp. 475–479. doi: 10.15388/LMR.2010.86.

Abstract

In the paper, we present the upper bound of Lp norms ∆p of the order (a1 + a2)/(DZ)-1/2for all 1 < p< ∞, of the normal approximation for a standardized random variable (Z - EZ)/√DZ, where the random variable Z = a1X + a2Y , a1 + a2 = 1, ai > 0, i = 1, 2, the random variable X is distributed by the Poisson distribution with the parameter λ > 0, and the random variable Y by the standard gamma distribution Γ (α, 0, 1) with the parameter α > 0.

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