A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion

DOI

10.2991/jsta.d.191105.001How to use a DOI?

Keywords

Modified negative binomial distribution; Overdispersion; Underdispersion; Maximum likelihood estimator; Sufficient statistics; Exponential family; Weighted geometric distribution

Abstract

In this paper, we introduce a new and useful discrete distribution (modified negative binomial distribution) and its statistical and probabilistic properties are discussed. This distribution is a three-parameter extension of the negative binomial distribution that generalizes some well-known discrete distributions (negative binomial and geometric). Various statistical and probabilistic properties were derived such as moments, probability and moment generating functions and maximum likelihood estimation of parameters. Modified negative binomial distribution is appealing from a theoretical point of view since it belongs to the exponential family as well as to the weighted negative binomial distributions family. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. Finally, a real numerical example is also considered for illustrative purpose.

Copyright

© 2019 The Authors. Published by Atlantis Press SARL.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Ghobad Barmalzan
AU  - Hadi Saboori
AU  - Sajad Kosari
PY  - 2019
DA  - 2019/11/28
TI  - A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion
JO  - Journal of Statistical Theory and Applications
SP  - 343
EP  - 350
VL  - 18
IS  - 4
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.191105.001
DO  - 10.2991/jsta.d.191105.001
ID  - Barmalzan2019
ER  -