Bayesian Premium Estimators for Mixture of Two Gamma Distributions Under Squared Error, Entropy and Linex Loss Functions: With Informative and Non Informative Priors

Abstract

In this paper, we consider the Zeghdoudi distribution as the conditional distribution of Xn | 𝜃, we focus on estimation of the Bayesian premium under three loss functions (squared error which is symmetric, Linex and entropy, which are asymmetric), using non-informative and informative priors (the extension of Jeffreys and Gamma priors) respectively. Because of its difficulty and non linearity, we use a numerical approximation for computing the Bayesian premium.

Keywords

• Zeghdoudi distribution
• gamma distribution
• loss function
• Bayesian premium