Multivariate Count Data Generalized Linear Models: Three Approaches Based on the Sarmanov Distribution
37 Pages Posted: 14 Nov 2017
Date Written: November 10, 2017
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: Suggested Citation