Moments of the Negative Multinomial Distribution
The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, general formulas for the falling factorial moments and cumulants of the negative multinomial distribution were obtained....
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/28/4/85 |
| _version_ | 1827729292447973376 |
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| author | Frédéric Ouimet |
| author_facet | Frédéric Ouimet |
| author_sort | Frédéric Ouimet |
| collection | DOAJ |
| description | The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, general formulas for the falling factorial moments and cumulants of the negative multinomial distribution were obtained. However, despite the availability of the moment generating function, no comprehensive formulas for the moments have been calculated thus far. This paper addresses this gap by presenting general formulas for both central and non-central moments of the negative multinomial distribution. These formulas are expressed in terms of binomial coefficients and Stirling numbers of the second kind. Utilizing these formulas, we provide explicit expressions for all central moments up to the fourth order and all non-central moments up to the eighth order. |
| first_indexed | 2024-03-10T23:45:54Z |
| format | Article |
| id | doaj.art-b7e40a72703a419c91f0796c1ad9b4da |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T23:45:54Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-b7e40a72703a419c91f0796c1ad9b4da2023-11-19T02:04:50ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472023-07-012848510.3390/mca28040085Moments of the Negative Multinomial DistributionFrédéric Ouimet0Centre de Recherches Mathématiques, Université de Montréal, Montreal, QC H3T 1J4, CanadaThe negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, general formulas for the falling factorial moments and cumulants of the negative multinomial distribution were obtained. However, despite the availability of the moment generating function, no comprehensive formulas for the moments have been calculated thus far. This paper addresses this gap by presenting general formulas for both central and non-central moments of the negative multinomial distribution. These formulas are expressed in terms of binomial coefficients and Stirling numbers of the second kind. Utilizing these formulas, we provide explicit expressions for all central moments up to the fourth order and all non-central moments up to the eighth order.https://www.mdpi.com/2297-8747/28/4/85negative multinomial distributionmomentscentral momentsnon-central moments |
| spellingShingle | Frédéric Ouimet Moments of the Negative Multinomial Distribution Mathematical and Computational Applications negative multinomial distribution moments central moments non-central moments |
| title | Moments of the Negative Multinomial Distribution |
| title_full | Moments of the Negative Multinomial Distribution |
| title_fullStr | Moments of the Negative Multinomial Distribution |
| title_full_unstemmed | Moments of the Negative Multinomial Distribution |
| title_short | Moments of the Negative Multinomial Distribution |
| title_sort | moments of the negative multinomial distribution |
| topic | negative multinomial distribution moments central moments non-central moments |
| url | https://www.mdpi.com/2297-8747/28/4/85 |
| work_keys_str_mv | AT fredericouimet momentsofthenegativemultinomialdistribution |