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.

Estimating the scale parameter of the Gumbel-Lomax Distribution using the Bayesian method of estimation and evaluating the estimators by assuming two non-informative prior distributions and one informative prior distribution is very important for the general application of the Gumbel-Lomax distribution. These estimators are obtained using the squared error loss function (SELF), Quadratic loss function (QLF) and precautionary loss function (PLF). The posterior distributions of the scale parameter of the Gumbel-Lomax distribution are derived and the Estimators are also obtained using the above mentioned priors and loss functions. Furthermore, a simulation using a package in R software is carried out to assess the performance of the estimators by making use of the Mean Squared Errors of the Estimators under the Bayesian approach and Maximum likelihood method. Our results show that Bayesian Method using PLF under all priors produces the best estimators of the scale parameter compared to estimators using the Maximum Likelihood method, SELF and QLF under all the priors irrespective of the values of the parameters and the different sample sizes. It is also discovered that the other parameters have no effect on the estimators of the scale parameter.

In this research a new extension of the Lomax distribution known as Lindley-Lomax distribution has been proposed by adding a shape parameter to the Lomax distribution using the Lindley-G family of distributions. The proposed article considered and extensively studied some properties of the new distribution such as moments, moment generating function, the characteristics function, survival function, hazard function and the distribution of order statistics. A graphical study of the proposed distribution and the other related functions was also done in the article. Estimation of the parameters of the proposed distribution was also done using the method of maximum likelihood estimation. The performance of the Lindley-Lomax distribution has also been tested by an application to the rate of mother-to-child HIV transmission.