Abstract
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. All numerical
computations and simulations were performed using MATLAB 2024b.
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. All numerical
computations and simulations were performed using MATLAB 2024b.
Keywords
Asymmetric loss functions.
Bayesian estimation
Exponential prior
hypothetical prior
Odd Chen–Gamma distribution