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.
Highlights
Credibility theory is a rating technique in actuarial science which can be seen as one of the quantitative tools that allow the insurers to perform experience rating, that is, to adjust future premiums based on past experiences
We focused on a popular tool in credibility theory which is the Bayesian premium estimator developed by [1], considering the Zeghdoudi distribution (ZD) as a claim distribution
The Bayesian premium PBSELF is the estimator of μ (θ), it is to be chosen such that the posterior expectation of the squared error loss function
Summary
Credibility theory is a rating technique in actuarial science which can be seen as one of the quantitative tools that allow the insurers to perform experience rating, that is, to adjust future premiums based on past experiences. We focused on a popular tool in credibility theory which is the Bayesian premium estimator developed by [1], considering the Zeghdoudi distribution (ZD) as a claim distribution. Metiri et al [16] explain the derivation of posterior distributions for the Lindley distribution under Linex loss functions using informative and non-informative priors.
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