A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data

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dc.contributor.authorOng, Seng Huat
dc.contributor.authorSim, Shin Zhu
dc.contributor.authorLiu, Shuangzhe
dc.contributor.authorSrivastava, Hari M.
dc.date.accessioned2023-10-06T14:21:33Z
dc.date.available2023-10-06T14:21:33Z
dc.date.copyright2023en_US
dc.date.issued2023
dc.description.abstractThis 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.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipThis research was funded by Ministry of Higher Education grant FRGS/1/2020/STG06/SYUC/02/1 and UCSI University grant REIG-FBM-2022/050.en_US
dc.identifier.citationOng, S. H., Sim, S. Z., Liu, S., & Srivastava, H. M. (2023). A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data. Stats, 6(3), 942–955. https://doi.org/10.3390/stats6030059en_US
dc.identifier.urihttps://doi.org/10.3390/stats6030059
dc.identifier.urihttp://hdl.handle.net/1828/15483
dc.language.isoenen_US
dc.publisherStatsen_US
dc.subjectconvolution
dc.subjectdispersion
dc.subjectConway–Maxwell–Poisson
dc.subjectgeneralized Poisson
dc.subjectinverse trino- mial
dc.subjectnegative binomial
dc.subjectgoodness-of-fit
dc.subjectog-concavity
dc.subjectparameter estimation
dc.subjectscore and likelihood ratio tests
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleA Family of Finite Mixture Distributions for Modelling Dispersion in Count Dataen_US
dc.typeArticleen_US

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