Beta generated Kumaraswamy-G and other new families of distributions

TL;DR

This paper introduces a new generalized distribution family based on Kumaraswamy-G, unifying several recent distributions, and explores its properties, estimation methods, and applications to real data.

Contribution

It proposes a novel beta generated Kumaraswamy-G distribution that encompasses multiple recent distribution families and derives its properties and estimation techniques.

Findings

Distribution effectively models real data sets.

Derived properties include moments, entropy, and quantiles.

Parameter estimation methods are validated with data.

Abstract

A new generalization of the family of Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution that includes three recently proposed families namely the Garhy generated family (Elgarhy et al., 2016), Beta-Dagum and Beta-Singh-Maddala distribution (Domma and Condino, 2016) is proposed by constructing beta generated Kumaraswamy-G distribution. Useful expansions of the pdf and the cdf of the proposed family is derived and seen as infinite mixtures of the Kumaraswamy-G distribution. Order statistics, Probability weighted moments, moment generating function, R\'enyi entropies, quantile power series, random sample generation, asymptotes and shapes are also investigated. Two methods of parameter estimation are presented. Suitability of the proposed model in comparisons to its sub models is carried out considering two real life data sets. Finally, some new classes of beta generated families are proposed for future investigations.