A New Family of Continuous Distributions: Properties, Copulas and Real Life Data Modeling

Abstract

A new family of distributions called the Kumaraswamy Rayleigh family is defied and studied. Some of its relevant statistical properties are derived. Many new bivariate type G families using the of Farlie-Gumbel-Morgenstern, modified Farlie-Gumbel-Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. The method of the maximum likelihood estimation is used. Some special models based on log-logistic, exponential, Weibull, Rayleigh, Pareto type II and Burr type X, Lindley distributions are presented and studied. Three dimensional skewness and kurtosis plots are presented. A graphical assessment is performed. Two real life applications to illustrate the flexibility, potentiality and importance of the new family is proposed.