Some approximation results for Bayesian Posteriors that involve the Hurwitz-Lerch Zeta distribution

Document Type

Article

Publication Date

3-1-2023

Abstract

Consider the generalized Poisson and the negative binomial model with mean parameter equal to kb, where k >= 0 is a count parameter and 0 < b < 1 is a hyper parameter. We show that conditioning on counts from both models and assuming a uniform prior fork lead to the following Bayesian posterior distributions: (i) geometric for conditioning value of 0; (ii) extended negative binomial for conditioning value of 1; (iii) approximately extended Hurwitz-Lerch zeta distribution for conditioning value of 2 or more. Kullback-Leibler divergence for measuring the quality of the approximating distributions for some combinations of b and the mean-variance ratio is given.

Keywords

Approximation, Generalized Poisson distribution, Hurwitz-Lerch zeta distribution, Negative binomial distribution, Posterior distribution

Publication Title

Bulletin of the Malaysian Mathematical Sciences Society

Divisions

Science,MathematicalSciences

Volume

46

Issue

2

Publisher

Springer Verlag

Publisher Location

CAMPUS, 4 CRINAN ST, LONDON, N1 9XW, ENGLAND

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