The Generalized Marshall-Olkin-Kumaraswamy-G family of distributions

TL;DR

This paper introduces a new flexible family of distributions based on Kumaraswamy-G and Marshall-Olkin methods, providing theoretical properties, estimation techniques, and real data application.

Contribution

It proposes the Generalized Marshall-Olkin-Kumaraswamy-G family of distributions, expanding the class of models with series expansions, properties, and estimation methods.

Findings

Derived series expansions for density and survival functions.

Provided parameter estimation methods with confidence intervals.

Applied the model to real data demonstrating its flexibility.

Abstract

A new family of distribution is proposed by using Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution as the base line distribution in the Generalized Marshal-Olkin (Jayakumar and Mathew, 2008) Construction. A number of special cases are presented. By expanding the probability density function and the survival function as infinite series the proposed family is seen as infinite mixtures of the Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution. Density function and its series expansions for order statistics are also obtained. Order statistics, moments, moment generating function, R\'enyi entropy, quantile function, random sample generation, asymptotes, shapes and stochastic orderings are also investigated. The methods of parameter estimation by method of maximum likelihood and method of moment are presented. Large sample standard error and confidence intervals for the mles are also discussed. One real life application of comparative data fitting with some of the important sub models of the family and some other models is considered.