Bayesian Estimation for Parameters of Power Function Distribution under Various Priors

Abstract

Although the idea of Bayesian inference dates back to the late 18th century, its use by statisticians has been rare until recently. But due to advancement in the simulation techniques Bayesian inference and estimation is gaining currency. This paper seeks to focus on the Bayesian estimates of the Power Function distribution using Weibull and Generalized Gamma distributions as priors for the unknown parameters. Furthermore, the statistical performance of the obtained estimators is compared with the Maximum likelihood of Power Function distribution and the Bayesian estimator of Gamma distribution as prior of the unknown parameter. The comparison has been done using Monte Carlo simulation using MSE as yardstick of the comparison.

Keywords: Squared error loss function, Bayesian estimator, Prior distribution, Monte Carlo simulation.