We introduce a three-parameter extension of the exponential distribution which contains as sub-models the exponential, logistic-exponential and Marshall-Olkin exponential distributions. The new model is very flexible and its associated density function can be decreasing or unimodal. Further, it can produce all of the four major shapes of the hazard rate, that is, increasing, decreasing, bathtub and upside-down bathtub. Given that closed-form expressions are available for the survival and hazard rate functions, the new distribution is quite tractable. It can be used to analyze various types of observations including censored data. Computable representations of the quantile function, ordinary and incomplete moments, generating function and probability density function of order statistics are obtained. The maximum likelihood method is utilized to estimate the model parameters. A simulation study is carried out to assess the performance of the maximum likelihood estimators. Two actual data sets are used to illustrate the applicability of the proposed model.

We introduce a new class of continuous distributions called the complementary generalized transmuted Poisson-G family, which extends the transmuted class pioneered by Shaw and Buckley (2007). We provide some special models and derive general mathematical properties including quantile function, explicit expressions for the ordinary and incomplete moments, generating function, Renyi and Shannon entropies and order statistics. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the new family is illustrated by means of two applications to real data sets.

A generalization of the Lindley distribution namely, Lindley negative-binomial distribution, is introduced. The Lindley and the exponentiated Lindley distributions are considered as sub-models of the proposed distribution. The proposed model has flexible density and hazard rate functions. The density function can be decreasing, right-skewed, left-skewed and approximately symmetric. The hazard rate function possesses various shapes including increasing, decreasing and bathtub. Furthermore, the survival and hazard rate functions have closed form representations which make this model tractable for censored data analysis. Some general properties of the proposed model are studied such as ordinary and incomplete moments, moment generating function, mean deviations, Lorenz and Bonferroni curve. The maximum likelihood and the Bayesian estimation methods are utilized to estimate the model parameters. In addition, a small simulation study is conducted in order to evaluate the performance of the estimation methods. Two real data sets are used to illustrate the applicability of the proposed model.