A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data
This paper considers the construction of a family of discrete distributions with the flexibility to cater for under-, equi- and over-dispersion in count data using a finite mixture model based on standard distributions. We are motivated to introduce this family because its simple finite mixture stru...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Stats |
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| Online Access: | https://www.mdpi.com/2571-905X/6/3/59 |
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| author | Seng Huat Ong Shin Zhu Sim Shuangzhe Liu Hari M. Srivastava |
| author_facet | Seng Huat Ong Shin Zhu Sim Shuangzhe Liu Hari M. Srivastava |
| author_sort | Seng Huat Ong |
| collection | DOAJ |
| description | This paper considers the construction of a family of discrete distributions with the flexibility to cater for under-, equi- and over-dispersion in count data using a finite mixture model based on standard distributions. We are motivated to introduce this family because its simple finite mixture structure adds flexibility and facilitates application and use in analysis. The family of distributions is exemplified using a mixture of negative binomial and shifted negative binomial distributions. Some basic and probabilistic properties are derived. We perform hypothesis testing for equi-dispersion and simulation studies of their power and consider parameter estimation via maximum likelihood and probability-generating-function-based methods. The utility of the distributions is illustrated via their application to real biological data sets exhibiting under-, equi- and over-dispersion. It is shown that the distribution fits better than the well-known generalized Poisson and COM–Poisson distributions for handling under-, equi- and over-dispersion in count data. |
| first_indexed | 2024-03-10T21:59:19Z |
| format | Article |
| id | doaj.art-5f06baf98f0445e6a2d9e4966ba3257e |
| institution | Directory Open Access Journal |
| issn | 2571-905X |
| language | English |
| last_indexed | 2024-03-10T21:59:19Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Stats |
| spelling | doaj.art-5f06baf98f0445e6a2d9e4966ba3257e2023-11-19T13:00:51ZengMDPI AGStats2571-905X2023-09-016394295510.3390/stats6030059A Family of Finite Mixture Distributions for Modelling Dispersion in Count DataSeng Huat Ong0Shin Zhu Sim1Shuangzhe Liu2Hari M. Srivastava3Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, MalaysiaSchool of Mathematical Sciences, University of Nottingham Malaysia, Semenyih 43500, MalaysiaFaculty of Science and Technology, University of Canberra, Bruce, ACT 2617, AustraliaDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaThis paper considers the construction of a family of discrete distributions with the flexibility to cater for under-, equi- and over-dispersion in count data using a finite mixture model based on standard distributions. We are motivated to introduce this family because its simple finite mixture structure adds flexibility and facilitates application and use in analysis. The family of distributions is exemplified using a mixture of negative binomial and shifted negative binomial distributions. Some basic and probabilistic properties are derived. We perform hypothesis testing for equi-dispersion and simulation studies of their power and consider parameter estimation via maximum likelihood and probability-generating-function-based methods. The utility of the distributions is illustrated via their application to real biological data sets exhibiting under-, equi- and over-dispersion. It is shown that the distribution fits better than the well-known generalized Poisson and COM–Poisson distributions for handling under-, equi- and over-dispersion in count data.https://www.mdpi.com/2571-905X/6/3/59convolutiondispersionConway–Maxwell–Poissongeneralized Poissoninverse trinomialnegative binomial |
| spellingShingle | Seng Huat Ong Shin Zhu Sim Shuangzhe Liu Hari M. Srivastava A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data Stats convolution dispersion Conway–Maxwell–Poisson generalized Poisson inverse trinomial negative binomial |
| title | A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data |
| title_full | A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data |
| title_fullStr | A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data |
| title_full_unstemmed | A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data |
| title_short | A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data |
| title_sort | family of finite mixture distributions for modelling dispersion in count data |
| topic | convolution dispersion Conway–Maxwell–Poisson generalized Poisson inverse trinomial negative binomial |
| url | https://www.mdpi.com/2571-905X/6/3/59 |
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