We propose a new generator of continuous distributions with one extra positive parameter called the odd Lindley-G family. Some special cases are presented. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Various structural properties of the new family, which hold for any baseline model, are derived including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, Rényi entropy, reliability, order statistics and their moments and k upper record values. We provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates. We discuss estimation of the model parameters by maximum likelihood and provide an application to a real data set.

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.

RESUMO. A família de distribuições univariadas gama-generalizada proposta por Zografos e Balakrishnan [3] foi discutida por Nadarajah et al. [7] que deram um amplo tratamento matemático a esta classe. Neste artigo, estudamos o modelo Gama Weibull Poisson, que tem como casos especiais, várias distribuições discutidas na literatura. Deduzimos uma expressão explícita para a entropia de Rényi, e mostramos que a densidade da distribuição Gama Weibull Poissoné uma mistura de densidades da distribuição Weibull Poisson. Estudamos algumas propriedades matemáticas importantes como momentos, função geratriz de momentos e função quantílica.

A new distribution called the exponentiated generalized Lindley is proposed and studied. This distribution includes as special cases the Lindley and exponentiated Lindley distributions. We study the main properties of this distribution, with special emphasis on its moments and some characteristics related to reliability studies. The estimation of the model parameters using the methods of moments and maximum likelihood is also discussed. The flexibility of this distribution is illustrated via an application to a real data set.

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.