In this article, we introduce a new class of five-parameter model called the Exponentiated Weibull Lomax arising from the Exponentiated Weibull generated family. The new class contains some existing distributions as well as some new models. Explicit expressions for its moments, distribution and density functions, moments of residual life function are derived. Furthermore, Rényi and q–entropies, probability weighted moments, and order statistics are obtained. Three suggested procedures of estimation, namely, the maximum likelihood, least squares and weigthed least squares are used to obtain the point estimators of the model parameters. Simulation study is performed to compare the performance of different estimates in terms of their relative biases and standard errors. In addition, an application to two real data sets demonstrate the usefulness of the new model comparing with some new models.
In this paper, a new version of the Poisson Lomax distributions is proposed and studied. The new density is expressed as a linear mixture of the Lomax densities. The failure rate function of the new model can be increasing-constant, increasing, U shape, decreasing and upside down-increasing. The statistical properties are derived and four applications are provided to illustrate the importance of the new density. The method of maximum likelihood is used to estimate the unknown parameters of the new density. Adequate fitting is provided by the new model.