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.
Highlights
Introduction and motivationRecently, there has been an exceptional eagerness for growing more flexible families of distributions by extending the classical cumulative distribution functions (CDFs)
In modeling real-life data, the new family proved its superiority against the special generalized mixture-G family, odd log-logistic-G family, Burr-Hatke-G family transmuted Topp-Leone-G family, gamma-G family, Kumaraswamy-G family, beta-G family and Exponentiated-G family
We introduce two formulae for the moment generating function
Summary
There has been an exceptional eagerness for growing more flexible families of distributions by extending the classical cumulative distribution functions (CDFs). 2. In modeling real-life data, the new family proved its superiority against the special generalized mixture-G family, odd log-logistic-G family, Burr-Hatke-G family transmuted Topp-Leone-G family, gamma-G family, Kumaraswamy-G family, beta-G family and Exponentiated-G family.
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