Estimation of a Shape Parameter of a Gompertz-lindley Distribution Using Bayesian and Maximum Likelihood Methods

The Gompertz-Lindley distribution is an extension of the Lindley distribution with three parameters. It was found to be more flexible for modeling real life events. The distribution contains two shape parameters and a scale parameter. Despite the necessity of parameter estimation theory in modeling, it has not been shown that a method of estimation method is better for any of these three parameters of the Gompertz-Lindley distribution. This paper identifies the best estimation method for the shape parameter of the Gompertz-Lindley distribution by deriving Bayesian estimators for the shape parameter of the distribution using two non-informative prior distributions (Uniform and Jeffery) and an informative prior (gamma) under squared error loss function (SELF), quadratic loss function (QLF) and precautionary loss function (PLF). These estimators were evaluated and the results compared with the maximum likelihood estimation method using Monte Carlo simulations with the mean square error (MSE) as a criterion for choosing the best estimator.