Bayesian Look at The Rare Event Distribution

Abstract

In this article, Bayesian analysis of parameter () of Poisson distribution under simulated data is conducted. Posterior distributions are obtained under two informative (Gamma and Exponential) and two non-informative (Uniform and Jaffrey’s) priors. Five loss functions including Square Error Loss Function (SELF), Weighted Square Error Loss Function (WSELF), LINEX Loss Function (LLF), Quasi Quadratic Loss Function (QQLF) and Precautionary Loss Function (PLF) are used to obtain the Bayes estimators and risks associated with them to study the performance and behavior of the Poisson parameter (). From this simulation study we found that gamma distribution is suitable prior for Poisson and Quasi Quadratic Loss Function provides efficient results compared to other Loss functions with minimum risks associated with these estimates.

Keywords

• bayesian analysis, poisson distribution, loss function, bayes risk, simulation