On the bivariate Sarmanov distribution and copula. An application on insurance data using truncated marginal distributions

Zuhair Bahraoui ^[1] ; Catalina Bolancé ^[1] ; Elena Pelican ^[2] ; Raluca Vernic ^[2]
1. [1] Universitat de Barcelona
  
  Universitat de Barcelona
  
  Barcelona, España
2. [2] Universitatea Ovidius din Constanta
Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 39, Nº. 2, 2015, págs. 209-230
Idioma: inglés
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Resumen
- The Sarmanov family of distributions can provide a good model for bivariate random variables and it is used to model dependency in a multivariate setting with given marginals. In this paper, we focus our attention on the bivariate Sarmanov distribution and copula with different truncated extreme value marginal distributions. We compare a global estimation method based on maximizing the full log-likelihood function with the estimation based on maximizing the pseudo-log-likelihood function for copula (or partial estimation). Our aim is to estimate two statistics that can be used to evaluate the risk of the sum exceeding a given value. Numerical results using a real data set from the motor insurance sector are presented.