Bayesian estimation under different loss functions for the case of inverse Rayleigh distribution

Abstract

In this study, the best parameter estimator for the scale parameter $\left(\theta \right)$ of the inverse Rayleigh distribution was determined based on a comparison of the maximum likelihood estimator (MLE) method, the Bayesian generalized squared error loss function (SELF), the Bayesian linear exponential loss function (LINEX LF), and the Bayesian entropy loss function (ELF). The prior distribution chosen was the non-informative prior, namely the Jeffrey prior, and the informative prior using the exponential distribution. The estimator evaluation method used was based on the smallest value of the Akaike information criterion (AIC), corrected Akaike information criterion (AICc), and Bayesian information criterion (BIC). Based on simulation studies and real data, it was found that the best parameter estimator on the data for the scale parameter $\left(\theta \right)$ of the inverse Rayleigh distribution is the Bayes ELF prior exponential $\left({\hat{\theta }}_{EE}\right)$.