Bayesian and Non-Bayesian Inference for The Generalized Power Akshaya Distribution with Application in Medical

Abstract

Generalized power Akshaya distribution is a brand-new two-parameter distribution that builds on the Akshaya distribution first introduced by \cite{Ramadan}. The lifetime data is intended to be modelled by this distribution. The generalised power Akshaya's parameters are estimated using both the conventional and Bayesian approaches in this work. The weighted least square estimation (WLSE), least square estimation (LSE), Cramer-von-Mises estimation (CVME), Anderson and Darling (AD) method of estimation, Maximum Product Space Estimators (MPSE), and maximum likelihood estimation (MLE), six traditional estimation methods, are used to find the model parameters. The parameters of the suggested distribution were also determined using the squared error loss function and Bayesian estimating (BE) under independent gamma priors. The unknown parameters have been estimated using the Bayesian approach using Markov chain Monte Carlo (MCMC). Additionally, the parameters' average width of the confidence intervals and coverage probability are computed. Additionally, the reliable intervals for Bayesian estimates of the unknown parameters calculated.