For the first time, a four-parameter lifetime model, called the gamma extended Fréchet distribution, is defined and studied. We obtain some of its mathematical properties. Explicit expressions for the ordinary and incomplete moments, quantile function, mean deviations, Rényi entropy and reliability are provided. The order statistics and their moments are derived. The method of maximum likelihood is used for estimating the model parameters. We determine the observed information matrix. An application to a real data set shows that the new distribution can provide a better fit than other classical lifetime models. We hope that this generalization may attract wider applications in reliability, biology and survival analysis.

A five-parameter model, called the Burr XII negative binomial distribution, is defined and studied. The new model contains as special cases some important lifetime distributions discussed in the literature, such as the log-logistic, Weibull, Pareto type II and Burr XII distributions, among several others. We derive the ordinary and incomplete moments, generating and quantile functions, mean deviations, reliability and two types of entropy. The order statistics and their moments are investigated. The method of maximum likelihood is proposed for estimating the model parameters. We obtain the observed information matrix. An application to real data demonstrates that the new distribution can provide a better fit than other classical lifetime models.

For any baseline continuous G distribution, we propose a new generalized family called the Kumaraswamy-G Poisson (denoted with the prefix "Kw-GP") with three extra positive parameters. Some special distributions in the new family such as the Kw-Weibull Poisson, Kw-gamma Poisson and Kw-beta Poisson distributions are introduced. We derive some mathematical properties of the new family including the ordinary moments, generating function and order statistics. The method of maximum likelihood is used to fit the distributions in the new family. We illustrate its potentiality by means of an application to a real data set.

A five-parameter distribution, called the exponentiated Burr XII Poisson distribution, is defined and studied. The model has as special sub-models some important lifetime distributions discussed in the literature, such as the logistic, log-logistic, Weibull, Burr XII and exponentiated Burr XII distributions, among several others. We derive the ordinary and incomplete moments, generating and quantile functions, Bonferroni and Lorenz curves, mean deviations, reliability and two types of entropy. The order statistics and their moments are investigated. The method of maximum likelihood is proposed for estimating the model parameters. We obtain the observed information matrix. An application to a real data set demonstrates that the new distribution can provide a better fit than other classical lifetime models. We hope that this generalization may attract wider applications in reliability, biology and survival analysis.

We propose the McDonald Lindley-Poisson distribution and derive some of its mathematical properties including explicit expressions for moments, generating and quantile functions, mean deviations, order statistics and their moments. Its model parameters are estimated by maximum likelihood. A simulation study investigates the performance of the estimates. The new distribution represents a more flexible model for lifetime data analysis than other existing models as proved empirically by means of two real data sets.