On the rBell family of distributions with actuarial applications

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<title>On the rBell family of distributions with actuarial applications</title>
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<namePart>Bhati, Deepesh</namePart>
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<namePart>Calderín-Ojeda, Enrique</namePart>
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<abstract displayLabel="Summary">In this paper, a new three-parameter discrete family of distributions, the  family, is introduced. The family is based on series expansion of the r-Bell polynomials. The proposed model generalises the classical Poisson and the recently proposed Bell and BellTouchard distributions. It exhibits interesting stochastic properties. Its probabilities can be computed by a recursive formula that allows us to calculate the probability function of the amount of aggregate claims in the collective risk model in terms of an integral equation. Univariate and bivariate regression models are presented. The former regression model is used to explain the number of out-of-use claims in an automobile insurance portfolio, by showing a good out-of-sample performance. The latter is used to describe the number of out-of-use and parking claims jointly. This family provides an alternative to other traditionally used distributions to describe count data such as the negative binomial and Poisson-inverse Gaussian models.

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<note type="statement of responsibility">Deepesh Bhati, Enrique Calderín-Ojeda</note>
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<topic>Cálculo actuarial</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080586447">
<topic>Modelo estocástico</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080603779">
<topic>Seguro de automóviles</topic>
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<title>Astin bulletin</title>
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<publisher>Belgium : ASTIN and AFIR Sections of the International Actuarial Association</publisher>
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<identifier type="issn">0515-0361</identifier>
<identifier type="local">MAP20077000420</identifier>
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<text>03/01/2022 Volumen 52 Número 1 - enero 2022 , p. 185-210</text>
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