Sule Lamido University Journal of Science and Technology (SLUJST) Vol. 1 No. 1 [June, 2020], pp. 164-174 164 Bayesian Analysis of shape parameter of the Exponentiated Inverse Rayleigh distribution Etini Inemesit Akpayang 1 , Jamilu Garba 2 1 Department of statistics, Ahmadu Bello University, Zaria, Nigeria, 2 Department of statistics, Ahmadu Bello University, Zaria, Nigeria, Email: princeakpayang@gmail.com, gyjamilu@gmail.com Abstract 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. Keywords: Bayes Estimators; Jeffrey’s Prior; Quadratic Loss Function; Precautionary Loss Function; Squared Error Loss Function; Monte Carlo simulation 1. Introduction The Inverse Rayleigh distribution which was introduced by Trayer (1964) has been seen by many researchers a better and more flexible distribution than the earlier distribution ie Rayleigh distribution which was named after Lord Rayleigh and many research has been done in this area to further improve the work of Trayer (1964) and many distributions have been introduced such as the modified inverse Rayleigh distribution which was introduced by Muhammad (2014), the transmuted inverse Rayleigh distribution by Afaq Ahmad and Ahmed (2014) and lately the exponentiated inverse Rayleigh distribution by Rao and Mbwambo (2019) which we take a keen interest to. The estimation of parameters of probability models is no new feat in statistical inferences and modelling as i t’s a necessary procedure to make relevant sense of situations where these models are applied, over the years researchers have gone extra miles to ensure better and more efficient methods of estimation of the parameter of this distributions are achieved, and in statistical estimation, there are clearly two sets of individuals with varying view of estimations some prefer the classical approach while others the Bayesians’ approach. This classes of estimation has been applied in vast fields over the years especially in reliability studies and life data analysis, though the most widely used method for estimating distribution parameters has been the maximum likelihood estimation due to its very relevant property for providing the best linear unbiased estimate but other estimators have their own salient properties that make them relevant and in recent times, Bayesian approach of statistical estimation has aroused great consideration by many researchers among them is Yahaya and Dewu (2017) in their study estimated the scale parameter of log-logistic distribution under the assumption of informative priors wherein the Bayes estimates and posterior risks were derived under squared error loss function(SELF) and precautionary loss function(PLF), Aliyu and Yahaya (2016) acquired the estimates of the shape parameter of the generalized Rayleigh distribution using the squared error, Entropy and Precautionary loss functions assuming