Bayesian Analysis of shape parameter of the Exponentiated Inverse Rayleigh distribution

Etini Inemesit Akpayang, Jamilu Garba

Keywords: Bayes Estimators; Jeffrey’s Prior; Quadratic Loss Function; Precautionary Loss Function; Squared Error Loss Function; Monte Carlo simulation


The exponentiated inverse Rayleigh distribution (EIRD) is a generalization of inverse Rayleigh distribution introduced by Rao & Mbwambo (2019). Rao & Mbwambo (2019) investigated different methods of parameter estimation such as maximum likelihood method, percentile-based method, least squares method and weighted least squares method and compare theirs estimates using extensive numerical simulations. In this work, however, we explore Bayesian techniques to parameter estimation using symmetric and asymmetric loss function under informative and non-informative priors and compared the results with the best of what was obtained by Rao & Mbwambo (2019). The result shows that: Bayes estimator under the square error loss function assuming Jeffreys prior gave the same estimates with maximum likelihood estimators but slightly different and better when Bayesian estimator under square error loss function assuming gamma prior is considered which is a better alternative to the classical estimator.