Exploring the Exponentiated Transmuted Inverse Rayleigh Distribution (ETIRD) in Classical and Bayesian Paradigms

Abstract

We derived, a new three parameters continuous probability distribution called Exponentiated Transmuted Inverse Rayleigh Distribution (ETIRD). Various mathematical properties of the new distribution including mean, rth moments, moment generating function, quantile function etc. are derived. In the Classical paradigm, the estimators of the distribution are obtained using the maximum likelihood method. The Bayes estimators are derived under square error loss function (SELF) using non-informative and informative priors via the Lindley approximation technique. Bayes Estimators are compared with their corresponding maximum likelihood Estimators (MLEs) using a Monte Carlo Simulation Study under different sample sizes, different values of true parameters, using informative and non-informative priors. Performance of Bayes estimators and classical estimates is judged for the four real life data sets. The results of simulation study and real-life example show that the Bayes estimators provided better results than MLEs.