This paper introduces a new four parameter Rayleigh distribution which generalizes the transmuted generalized Rayleigh distribution introduced by Merovci (2014). The new model is referred to as exponentiated transmuted generalized Rayleigh (ETGR) distribution. Various mathematical properties of the new model including ordinary and incomplete moments, quantile function, generating function and Rényi entropy are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. Two real data sets are used to compare the flexibility of the new model versus other models.

This paper introduces a new generalization of the transmuted Marshall-Olkin Fréchet distribution of , using Kumaraswamy generalized family. The new model is referred to as Kumaraswamy transmuted Marshall-Olkin Fréchet distribution. This model contains sixty two sub-models as special cases such as the Kumaraswamy transmuted Fréchet, Kumaraswamy transmuted Marshall-Olkin, generalized inverse Weibull and Kumaraswamy Gumbel type II distributions, among others. Various mathematical properties of the proposed distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Rényi and -entropies are derived. The unknown parameters of the new distribution are estimated using the maximum likelihood estimation. We illustrate the importance of the new model by means of two applications to real data sets.

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.

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