Bayesian Estimation for Deformed Modified Power Series Distribution

Abstract

In this article, posterior distribution, posterior moments, and predictive distribution for the modified power series distributions deformed at any of a support point under linex and generalized entropy loss function are derived. It is assumed that the prior information can be summarized by a uniform, Beta, two-sided power, Gamma, or generalized Pareto distributions. The obtained results are demonstrated on the generalized Poisson and the generalized negative binomial distribution deformed at a given point.

Keywords:

• Bayesian estimator
• Deformed distribution
• Generalized entropy loss function
• Linex loss function
• Power series distribution
• Posterior distribution
• Posterior moments
• Predictive distribution

Mathematics Subject Classification:

• 62C10
• 62F15