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.

In this work, we introduce a new Poisson-log-logistic distribution with a physical interpretation and some applications. Some essential properties are derived. Modeling of four real data sets are provided to illustrate the wide applicability of the new model in differnt fields like finance, reliability, economy and medicine. The new compound model is better than other well-known competitive models which have at least the same number of parameters.