The Marshall-Olkin-Kumarswamy-G family of distributions

TL;DR

This paper introduces a new family of continuous distributions based on Kumaraswamy-G and Marshall-Olkin constructions, exploring their properties, estimation methods, and applications to real data.

Contribution

It proposes a novel distribution family combining Kumaraswamy-G and Marshall-Olkin methods, with detailed properties, estimation techniques, and real data applications.

Findings

Derived various properties including moments, entropy, and quantile functions.

Compared two members of the family with existing models using real data.

Provided maximum likelihood and method of moments estimation results.

Abstract

A new family of continuous distribution is proposed by using Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution as the base line distribution in the Marshal-Olkin (Marshall and Olkin, 1997) 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, Renyi entropy, quantile function and random sample generation have been investigated. Asymptotes, shapes and stochastic ordering are also investigated. The parameter estimation by methods of maximum likelihood, their large sample standard errors and confidence intervals and method of moment are also presented. Two members of the proposed family are compared with corresponding members of Kumaraswamy-Marshal-Olkin-G family (Alizadeh et al., 2015) by fitting of two real life data sets.