{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T07:19:08Z","timestamp":1774595948223,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,30]],"date-time":"2021-12-30T00:00:00Z","timestamp":1640822400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this article we present a class of mixed Poisson regression models with varying dispersion arising from non-conjugate to the Poisson mixing distributions for modelling overdispersed claim counts in non-life insurance. The proposed family of models combined with the adopted modelling framework can provide sufficient flexibility for dealing with different levels of overdispersion. For illustrative purposes, the Poisson-lognormal regression model with regression structures on both its mean and dispersion parameters is employed for modelling claim count data from a motor insurance portfolio. Maximum likelihood estimation is carried out via an expectation-maximization type algorithm, which is developed for the proposed family of models and is demonstrated to perform satisfactorily.<\/jats:p>","DOI":"10.3390\/a15010016","type":"journal-article","created":{"date-parts":[[2021,12,30]],"date-time":"2021-12-30T21:41:21Z","timestamp":1640900481000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Mixed Poisson Regression Models with Varying Dispersion Arising from Non-Conjugate Mixing Distributions"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4072-1454","authenticated-orcid":false,"given":"George","family":"Tzougas","sequence":"first","affiliation":[{"name":"Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh TD1 3HE, UK"},{"name":"Department of Statistics, London School of Economics and Political Science, London TD1 3HE, UK"}]},{"given":"Natalia","family":"Hong","sequence":"additional","affiliation":[{"name":"Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh TD1 3HE, UK"}]},{"given":"Ryan","family":"Ho","sequence":"additional","affiliation":[{"name":"Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh TD1 3HE, UK"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"209","DOI":"10.2307\/3314912","article-title":"Negative binomial and mixed Poisson regression","volume":"15","author":"Lawless","year":"1987","journal-title":"Can. 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