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.

## 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 |
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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 |

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