Comparison of Classical and Bayesian methods to Estimate the shape parameter and Reliability function in Burr type X or two parameter of exponential Rayleigh distribution under different Loss function

Abstract

The paper deals with estimation shape parameter of Burr distribution type X (which also called two parameter exponential Rayleigh).The methods of estimation are Maximum likelihood method and percentiles estimator (PER), as well as Bayesian estimator using Jeffery's prior distribution. The Bayes estimator of shape parameter (θ) is conducted using different loss function, like squared error loss function and also precautionary loss function .The comparison is done using statistical Measures Mean Square error (MSE) take different sample size (n=15,30,50,100) and different set of initial values for (θ,λ)