Six-parameters exponential Pareto-Fréchet (EPF) distribution: Properties and applications

In this paper, A new six-parameter distribution called the Six-Parameters Exponential Pareto-Fréchet (EPF) distribution is derived. The new distribution is mixture of Exponential-Pareto and Fréchet distributions. we have been derived a few statistical properties of the new probability distribution. The shape of its density function for different values of the parameters has also been established. The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. Six-Parameters Exponential-Pareto and Fréchet (EPF) distribution were estimated by using maximum likelihood method. The flexibility of the Six-parameters Exponential-Pareto and Fréchet (EPF) distribution was shown by fitting the distribution to one real life data set. The goodness of fit shows that the new distribution outperforms the one parameter Exponential (ED) distribution, three parameter Lindely distribution(TPLD), Gamma distribution and invers Gamma distribution (IGD) for the data set used for this study.