Bayesian and Maximum Likelihood Estimation of the Shape Parameter of Exponential Inverse Exponential Distribution: A Comparative Approach
Innocent Boyle Eraikhuemen *
Department of Physical Sciences, Benson Idahosa University, Benin City, Nigeria.
Fadimatu Bawuro Mohammed
Department of Statistics, College of Science and Technology, Adamawa State Polytechnic Yola, Nigeria.
Ahmed Askira Sule
Department of Statistics, Ramat Polytechnic Maiduguri, Borno State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper aims at making Bayesian analysis on the shape parameter of the exponential inverse exponential distribution using informative and non-informative priors. Bayesian estimation was carried out through a Monte Carlo study under 10,000 replications. To assess the effects of the assumed prior distributions and loss function on the Bayesian estimators, the mean square error has been used as a criterion. Overall, simulation results indicate that Bayesian estimation under QLF outperforms the maximum likelihood estimation and Bayesian estimation under alternative loss functions irrespective of the nature of the prior and the sample size. Also, for large sample sizes, all methods perform equally well.
Keywords: Exponential inverse exponential distribution, Bayesian analysis, prior distributions, loss functions, mean square error.