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This paper proposes the Topp-Leone Gompertz distribution; an extension of the Gompertz distribution for modeling real life time data. The new model is obtained by transforming the cumulative distribution function of the Gompertz random variable, while taking the Topp-Leone as the generator. Some statistical properties of the new distribution are derived. Maximum likelihood estimates of model parameters are also derived. A Monte Carlo simulation study is carried out to examine the accuracy of the maximum likelihood estimate of the distribution parameters. Two real data sets are used to illustrate the applicability of the new distribution, and the results show that the new distribution outperforms some related lifetime distributions.

In this article, a new class of distribution of the exponential family of distributions called the Gompertz extended generalized exponential (G-EGE) distribution for life time processes is proposed. The mathematical properties of the G-EGE distribution such as reliability, hazard rate function, reversed hazard, cumulative, odd functions, quantiles function, kurtosis, skewness and order statistics were derived. The parameters of the G-EGE distribution were estimated using the maximum likelihood method. The e¢ ciency and ‡exibility of the G-EGE distribution were examined using a simulation study and a real life data application. The results revealed that the G-EGE distribution outperformed some existing distributions in terms of their test statistics.

This study introduces a parsimonious and tractable generator for continuous distribution called the Teissier-G family of distributions for continuous random variables and examines the distributions belonging to this family as the sub-models. Some general statistical characteristics and sub-models of the new generator were examined and studied. Similarly, we examined the shapes of the sub-models probability density function (pdf) and hazard rate function were investigated. The parameter of the proposed model was obtained in a closed form by maximum likelihood. In addition to the numerical real life applications, Monte Carlo simulation was performed to examine the flexibility of the introduced models. The models provide good fits in all the cases. The results show great improvement compared to existing models.

Highlights• This paper present a new mixture probability distribution.• The aim of the proposed distribution is to present a more flexible model for lifetime data.• Some important properties of the proposed distribution are studied.• Simulation study is carried out to examine the accuracy of the MLE for different sample sizes.• The usefulness of this distribution is examined with some real lifetime data from literature.