The Marshall-Olkin-Kumaraswamy-G family of distributions

Abstract

A new family of continuous probability distributions is proposed by using Kumaraswamy-G distribution as the base line distribution in the Marshall-Olkin construction. A number of known distributions are derived as particular cases. Various properties of the proposed family like formulation of the pdf as different mixture of exponentiated baseline distributions, order statistics, moments, moment generating function, Rényi entropy, quantile function and random sample generation have been investigated. Asymptotes, shapes and stochastic ordering are also investigated. Characterizations of the proposed family based on truncated moments, hazard function and reverse hazard function are also presented. The parameter estimation by method of maximum likelihood, their large sample standard errors and confidence intervals and method of moment are also discussed. Two members of the proposed family are compared with different sub models and also with the corresponding members of Kumaraswamy-Marshall-Olkin-G family by fitting of two real life data sets.

Keywords

• Exponentiated family; Power weighted moment; Characterizations; AIC; BIC; CAIC; HQIC and K-S test.