Multivariate Count Data Generalized Linear Models: Three Approaches Based on the Sarmanov Distribution

XREAP 2017-07

37 Pages Posted: 14 Nov 2017

See all articles by Catalina Bolancé

Catalina Bolancé

University of Barcelona - Department of Econometrics

Raluca Vernic

Ovidius University of Constanta

Date Written: November 10, 2017

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

Suggested Citation

Bolancé, Catalina and Vernic, Raluca, Multivariate Count Data Generalized Linear Models: Three Approaches Based on the Sarmanov Distribution (November 10, 2017). XREAP 2017-07, Available at SSRN: https://ssrn.com/abstract=3069467 or http://dx.doi.org/10.2139/ssrn.3069467

Catalina Bolancé (Contact Author)

University of Barcelona - Department of Econometrics ( email )

Av. Diagonal 690
Barcelona, E-08034
Spain

Raluca Vernic

Ovidius University of Constanta ( email )

b-dul Mamaia nr. 124
Constanta, 900527
Romania

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