Journal of Statistical Theory and Applications

Volume 18, Issue 4, December 2019, Pages 343 - 350

A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion

Authors
Ghobad Barmalzan*, Hadi Saboori, Sajad Kosari
Department of Statistics, University of Zabol, Sistan and Baluchestan, Iran
*Corresponding author. Email: ghobad.barmalzan@gmail.com
Corresponding Author
Ghobad Barmalzan
Received 6 January 2018, Accepted 27 August 2018, Available Online 28 November 2019.
DOI
https://doi.org/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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Journal
Journal of Statistical Theory and Applications
Volume-Issue
18 - 4
Pages
343 - 350
Publication Date
2019/11
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.d.191105.001How to use a DOI?
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/).

Cite this article

TY  - JOUR
AU  - Ghobad Barmalzan
AU  - Hadi Saboori
AU  - Sajad Kosari
PY  - 2019
DA  - 2019/11
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  - https://doi.org/10.2991/jsta.d.191105.001
ID  - Barmalzan2019
ER  -