Bayes Estimators of Exponentiated Inverse Rayleigh Distribution using Lindleys Approximation
Bashiru Omeiza Sule *
Department of Mathematical Sciences, Kogi State University, Anyigba, Kogi State, Nigeria.
Taiwo Mobolaji Adegoke *
Department of Statistics, University of Ilorin, Kwara State, Nigeria.
Kafayat Tolani Uthman
National Center for Genetic Resources and Biotechnology, Ibadan, Oyo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, Bayes estimators of the unknown shape and scale parameters of the Exponentiated Inverse Rayleigh Distribution (EIRD) have been derived using both the frequentist and bayesian methods. The Bayes theorem was adopted to obtain the posterior distribution of the shape and scale parameters of an Exponentiated Inverse Rayleigh Distribution (EIRD) using both conjugate and non-conjugate prior distribution under different loss functions (such as Entropy Loss Function, Linex Loss Function and Scale Invariant Squared Error Loss Function). The posterior distribution derived for both shape and scale parameters are intractable and a Lindley approximation was adopted to obtain the parameters of interest. The loss function were employed to obtain the estimates for both scale and shape parameters with an assumption that the both scale and shape parameters are unknown and independent. Also the Bayes estimate for the simulated datasets and real life datasets were obtained. The Bayes estimates obtained under dierent loss functions are close to the true parameter value of the shape and scale parameters. The estimators are then compared in terms of their Mean Square Error (MSE) using R programming language. We deduce that the MSE reduces as the sample size (n) increases.
Keywords: Lindley's approximation, posterior distribution, prior distribution, entropy loss function, linex loss function, scale invariant squared error loss function