The Kumaraswamy Generalized Marshall-Olkin-G family of distributions

TL;DR

This paper introduces a new family of continuous probability distributions based on the Generalized Marshall-Olkin and Kumaraswamy-G distributions, providing series expressions, moments, estimation methods, and real data applications.

Contribution

It proposes a novel distribution family combining Generalized Marshall-Olkin and Kumaraswamy-G, with comprehensive properties and estimation techniques, extending previous models.

Findings

Series expressions for pdf and survival functions

Parameter estimation via maximum likelihood and moments

Model comparison with real data examples

Abstract

Another new family of continuous probability distribution is proposed by using Generalized Marshal-Olkin distribution as the base line distribution in the Kumaraswamy-G distribution. This family includes (Cordeiro and de Castro, 2011) and (Jayakumar and Mathew, 2008) families special case besides a under of other distributions. The probability density function (pdf) and the survival function (sf) are expressed as series to observe as a mixture of the Generalized Marshal-Olkin distribution. Series expansions pdf of order statistics are also obtained. Moments, moment generating function, R\'enyi entropies, quantile function, random sample generation and asymptotes are also investigated. Parameter estimation by method of maximum likelihood and method of moment are also presented. Finally the proposed model is compared to the Generalized Marshall-Olkin Kumaraswamy extended family (Handique and Chakraborty, 2015) by considering four examples of real life data modeling.