A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion
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 discret...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer
2019-11-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/125924020/view |
| _version_ | 1818006433915994112 |
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| author | Ghobad Barmalzan Hadi Saboori Sajad Kosari |
| author_facet | Ghobad Barmalzan Hadi Saboori Sajad Kosari |
| author_sort | Ghobad Barmalzan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T05:01:07Z |
| format | Article |
| id | doaj.art-dd997cd097ad40108831307b4308f927 |
| institution | Directory Open Access Journal |
| issn | 2214-1766 |
| language | English |
| last_indexed | 2024-04-14T05:01:07Z |
| publishDate | 2019-11-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-dd997cd097ad40108831307b4308f9272022-12-22T02:10:57ZengSpringerJournal of Statistical Theory and Applications (JSTA)2214-17662019-11-0118410.2991/jsta.d.191105.001A Modified Negative Binomial Distribution: Properties, Overdispersion and UnderdispersionGhobad BarmalzanHadi SabooriSajad KosariIn 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.https://www.atlantis-press.com/article/125924020/viewModified negative binomial distributionOverdispersionUnderdispersionMaximum likelihood estimatorSufficient statisticsExponential family |
| spellingShingle | Ghobad Barmalzan Hadi Saboori Sajad Kosari A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion Journal of Statistical Theory and Applications (JSTA) Modified negative binomial distribution Overdispersion Underdispersion Maximum likelihood estimator Sufficient statistics Exponential family |
| title | A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion |
| title_full | A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion |
| title_fullStr | A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion |
| title_full_unstemmed | A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion |
| title_short | A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion |
| title_sort | modified negative binomial distribution properties overdispersion and underdispersion |
| topic | Modified negative binomial distribution Overdispersion Underdispersion Maximum likelihood estimator Sufficient statistics Exponential family |
| url | https://www.atlantis-press.com/article/125924020/view |
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