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

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 poste...

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Main Authors: Li, Hongxiang, Khang, Tsung Fei
Format: Article
Published: Springer Verlag 2023
Subjects:
Q Science (General)
QA Mathematics
Online Access:http://eprints.um.edu.my/38521/
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spelling my.um.eprints.385212024-08-06T07:37:14Z http://eprints.um.edu.my/38521/ Some approximation results for Bayesian Posteriors that involve the Hurwitz-Lerch Zeta distribution Li, Hongxiang Khang, Tsung Fei Q Science (General) QA Mathematics 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. Springer Verlag 2023-03 Article PeerReviewed 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 <https://doi.org/10.1007/s40840-023-01463-9>. 10.1007/s40840-023-01463-9
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic Q Science (General)
QA Mathematics
spellingShingle Q Science (General)
QA Mathematics
Li, Hongxiang
Khang, Tsung Fei
Some approximation results for Bayesian Posteriors that involve the Hurwitz-Lerch Zeta distribution
description 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.
format Article
author Li, Hongxiang
Khang, Tsung Fei
author_facet Li, Hongxiang
Khang, Tsung Fei
author_sort Li, Hongxiang
title Some approximation results for Bayesian Posteriors that involve the Hurwitz-Lerch Zeta distribution
title_short Some approximation results for Bayesian Posteriors that involve the Hurwitz-Lerch Zeta distribution
title_full Some approximation results for Bayesian Posteriors that involve the Hurwitz-Lerch Zeta distribution
title_fullStr Some approximation results for Bayesian Posteriors that involve the Hurwitz-Lerch Zeta distribution
title_full_unstemmed Some approximation results for Bayesian Posteriors that involve the Hurwitz-Lerch Zeta distribution
title_sort some approximation results for bayesian posteriors that involve the hurwitz-lerch zeta distribution
publisher Springer Verlag
publishDate 2023
url http://eprints.um.edu.my/38521/
_version_ 1806688798856183808
score 13.209306

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