This article aims at estimating the scale parameter of the Weimal distribution using Bayesian method and comparing the estimators obtained to the estimator of the scale parameter obtained from the method of maximum likelihood. Under Bayesian approach, the estimators are obtained by using uniform prior and Jeffrey’s prior with the adoption of the precautionary, quadratic and square error loss functions. A derivation and discussion2ws under maximum likelihood estimation is also done. The above methods of estimation employed in this paper are compared based on their mean square errors (MSEs) through a simulation study carried out in R statistical software with different sample sizes. The results indicate that the most appropriate method for the scale parameter is precautionary loss function under either uniform or Jeffrey’s prior irrespective of the sample sizes allocated and the values taken by the other parameters.

The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.

This article presents a comprehensive study of an odd Lindley-Gompertz distribution which has already been proposed in the literature but without any properties. The present study unlike the previous one has considered the derivation of several properties of the odd Lindley-Gompertz distribution with their graphical representations and discussions which has not been done in the first proposition of the distribution.  The study looks at properties such as survival (or reliability) function, the hazard function, the cumulative hazard function, the reverse hazard function, the odds function, quantile function, moments, moment generating function, characteristic function, cumulant generating function, distribution of order statistics and maximum likelihood estimation of the distribution’s parameters none of which was treated by the previous author of the model. An illustration to evaluate the goodness-of-fit of the odd Lindley-Gompertz distribution has also been done using two real life datasets and the results show that the model fits the datasets better than the five other distributions considered in this present study.