The compound class of extended Weibull power series distributions

TL;DR

This paper introduces a new class of extended Weibull power series distributions, encompassing numerous sub-models, with detailed properties, estimation methods, and real data application demonstrating its flexibility.

Contribution

It proposes a novel class of distributions by compounding extended Weibull and power series, including 68 sub-models and analyzing their properties and estimation techniques.

Findings

Includes 68 new sub-models within the class.

Provides mathematical properties like moments and generating functions.

Demonstrates applicability through real data analysis.

Abstract

In this paper, we introduce a new class of distributions which is obtained by compounding the extended Weibull and power series distributions. The compounding procedure follows the same set-up carried out by Adamidis and Loukas (1998) and defines at least new 68 sub-models. This class includes some well-known mixing distributions, such as the Weibull power series (Morais and Barreto-Souza, 2010) and exponential power series (Chahkandi and Ganjali, 2009) distributions. Some mathematical properties of the new class are studied including moments and generating function. We provide the density function of the order statistics and obtain their moments. The method of maximum likelihood is used for estimating the model parameters and an EM algorithm is proposed for computing the estimates. Special distributions are investigated in some detail. An application to a real data set is given to show the flexibility and potentiality of the new class of distributions.