The Beta Generalized Marshall-Olkin-G Family of Distributions

TL;DR

This paper introduces a new family of distributions based on the Beta-G construction with the Generalized Marshall-Olkin distribution, providing a flexible model with various statistical properties and applications to real data.

Contribution

It proposes a novel distribution family incorporating the Generalized Marshall-Olkin distribution into the Beta-G framework, including derivations, properties, and data fitting methods.

Findings

Derived series expansions for order statistics.

Compared the new model with existing distributions using real data.

Provided parameter estimation techniques and statistical properties.

Abstract

In this paper we propose a new family of distribution considering Generalized Marshal-Olkin distribution as the base line distribution in the Beta-G family of Construction. The new family includes Beta-G (Eugene et al. 2002 and Jones, 2004) and (Jayakumar and Mathew, 2008) families as particular cases. Probability density function (pdf) and the cumulative distribution function (cdf) are expressed as mixture of the Marshal-Olkin (Marshal and Olkin, 1997) distribution. Series expansions of pdf of the order statistics are also obtained. Moments, moment generating function, R\'enyi entropies, quantile power series, random sample generation and asymptotes are also investigated. Parameter estimation by method of maximum likelihood and method of moment are also presented. Finally proposed model is compared to the Generalized Marshall-Olkin Kumaraswamy extended family (Handique and Chakraborty, 2015) by considering three data fitting examples with real life data sets.