Bayesian Estimation Under Various Loss Functions With Application to the Odd Kappa–Exponential Distribution

This work examines Bayesian estimations of the reliability function and the parameters of the Odd Kappa–Exponential distribution using different symmetric and asymmetric loss functions. Bayes estimates are obtained by using squared log error, linear exponential, and El-Sayyad loss functions, contingent upon appropriate priors for the parameters. We compute Bayes estimates using Lindley’s approximation approach since they do not have closed forms under these loss functions. We derive the Bayes estimates through the Markov Chain Monte Carlo (MCMC) technique by employing the Metropolis–Hastings algorithm. The suggested estimators’ performances under the given loss functions are evaluated using simulation studies. Lastly, an analysis of a real data set is shown for illustration.