This paper uses a power transformation approach to introduce a three-parameter probability distribution which gives another extension of the Gompertz distribution known as “Power Gompertz distribution”. The statistical features of the power Gompertz distribution are systematically derived and studied appropriately. The three parameters of the new model are being estimated using the method of maximum likelihood estimation. The proposed distribution has also been compared to the Gompertz distribution using a real life dataset and the result shows that the Power Gompertz distribution has better performance than the Gompertz distribution and hence will be more useful and effective if applied in some real life situations especially survival analysis and cure fraction modeling just like the conventional Gompertz distribution.

The Gompertz inverse exponential distribution is a three-parameter lifetime model with greater flexibility and performance for analyzing real life data. It has one scale parameter and two shape parameters responsible for the flexibility of the distribution. Despite the importance and necessity of parameter estimation in model fitting and application, it has not been established that a particular estimation method is better for any of these three parameters of the Gompertz inverse exponential distribution. This article focuses on the development of Bayesian estimators for a shape of the Gompertz inverse exponential distribution using two non-informative prior distributions (Jeffery and Uniform) and one informative prior distribution (Gamma prior) under Square error loss function (SELF), Quadratic loss function (QLF) and Precautionary loss function (PLF). These results are compared with the maximum likelihood counterpart using Monte Carlo simulations. Our results indicate that Bayesian estimators under Quadratic loss function (QLF) with any of the three prior distributions provide the smallest mean square error for all sample sizes and different values of parameters.