The goal of this work is to introduce a new family of continuous distributions with a strong physical applications. Some statistical properties are derived, and certain useful characterizations of the proposed family of distributions are presented. Five applications are provided to illustrate the importance of the new family. A modified goodness-of-fit test for the new family in complete data case are investigated via two examples. We propose, as a first step, the construction of Nikulin-Rao-Robson statistic based on chi-squared fit tests for the new family in the case of complete data. The new test is based on the Nikulin-Rao-Robson statistic separately proposed by [

We study a new family of distributions defined by the minimum of the Poisson random number of independent and identically distributed random variables having the Topp Leone-G distribution. Some mathematical properties of the new family are derived. Maximum likelihood estimation of the model parameters is investigated. Two special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of the proposed family. In order to test the validity of the new family, a modified Chi-squared goodness-of-fit test based on Nikulin-Rao-Robson statistics is proposed theoretically.

A new distribution called the Weibull Generalized log logistic distribution is introduced along with a simple physical motivation. Several of its statistical properties are derived. Three applications are provided to illustrate the importance of the new distribution. The new distribution is shown to be better that other important competitive models via three applications. The method of maximum likelihood is used to estimate the unknown parameters.

We define and study a new class of continuous distributions called the Poisson-family. We present three of its several special models. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions and entropies are provided. The estimations of the model parameters is carried out using maximum likelihood method. The flexibility of the new family is illustrated by means of two applications to real data sets.

We define and study a new continuous distribution called the exponentiated Weibull Burr XII. Its density function can be expressed as a linear mixture of Burr XII. Its hazard rate is very flexibile in accomodating various shapes including constant, decreasing, increasing, J-shape, unimodal or bathtub shapes. Various of its structural properties are investigated including explicit expressions for the ordinary and incomplete moments, generating function, mean residual life, mean inactivity time and order statistics. We adopted the maximum likelihood method for estimating the model parameters. The flexibility of the new family is illustrated by means of a real data application.