Bayesian Estimation For The Odd Chen–Gamma Distribution Under Asymmetric Loss Functions

In this study, a new two-parameter lifetime distribution called the Odd Chen–Gamma distribution is proposed. The probability density function, cumulative distribution function, reliability function, and several important statistical properties of this distribution are derived. Bayesian analysis is performed using two prior functions for the unknown shape parameter: the exponential (informative) prior and a hypothetical prior. The Bayesian estimator of the shape parameter is obtained under two asymmetric loss functions, namely the De-Groot and the Al-Bayyati loss function. A simulation study is conducted to evaluate the performance of the Bayesian estimators by examining their mean squared errors under different parameter values and various sample sizes.