A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion
- Ghobad Barmalzan*, Hadi Saboori, Sajad KosariDepartment of Statistics, University of Zabol, Sistan and Baluchestan, Iran*Corresponding author. Email: firstname.lastname@example.org
- Corresponding Author
- Ghobad Barmalzan
- https://doi.org/10.2991/jsta.d.191105.001How to use a DOI?
- Modified negative binomial distribution, Overdispersion, Underdispersion, Maximum likelihood estimator, Sufficient statistics, Exponential family, Weighted geometric distribution
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.
- © 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 -