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

Li, Hongxiang and Khang, Tsung Fei (2023) Some approximation results for Bayesian Posteriors that involve the Hurwitz-Lerch Zeta distribution. Bulletin of the Malaysian Mathematical Sciences Society, 46 (2). ISSN 0126-6705, DOI https://doi.org/10.1007/s40840-023-01463-9.

Full text not available from this repository.

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.

Item Type: Article
Funders: UNSPECIFIED
Uncontrolled Keywords: Approximation; Generalized Poisson distribution; Hurwitz-Lerch zeta distribution; Negative binomial distribution; Posterior distribution
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Faculty of Science
Faculty of Science > Institute of Mathematical Sciences
Depositing User: Ms Zaharah Ramly
Date Deposited: 06 Aug 2024 07:35
Last Modified: 06 Aug 2024 07:37
URI: http://eprints.um.edu.my/id/eprint/38521

Actions (login required)

View Item View Item