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
Divisions
Science,MathematicalSciences
Publication Title
Bulletin of the Malaysian Mathematical Sciences Society
Volume
46
Issue
2
Publisher
Springer Verlag
Publisher Location
CAMPUS, 4 CRINAN ST, LONDON, N1 9XW, ENGLAND