Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution

Catalina Bolancé () and Raluca Vernic ()
Additional contact information
Catalina Bolancé: Research group–IREA. Av. Diagonal 696; 08034 Barcelona ,Spain.
Raluca Vernic: Faculty of Mathematics and Informatics Ovidius University of Constanta; Bd Mamaia 124, 900527 Constanta, Romania.

No 201718, IREA Working Papers from University of Barcelona, Research Institute of Applied Economics

Abstract: Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals and incorporate various individual characteristics of the policyholders by means of explanatory variables. Since the data set was collected over a longer time period (10 years), we also added each individual’s exposure to risk. To estimate the parameters of the three Sarmanov distributions, we analyze a pseudo-maximumlikelihood method. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM.

Keywords: Multivariate counting distribution; Sarmanov distribution; Negative Binomial distribution; Generalized Linear Model; ML estimation algorithm. JEL classification: C51; G22. (search for similar items in EconPapers)
Pages: 25 pages
Date: 2017-10, Revised 2017-10
New Economics Papers: this item is included in nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:ira:wpaper:201718

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