General Results for the Transmuted Family of Distributions and New Models

Marcelo Bourguignon,Indranil Ghosh,Gauss M Cordeiro

doi:10.1155/2016/7208425

Abstract

The transmuted family of distributions has been receiving increased attention over the last few years. For a baselineGdistribution, we derive a simple representation for the transmuted-Gfamily density function as a linear mixture of theGand exponentiated-Gdensities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, Rényi and Shannon entropies, and order statistics and their moments. We estimate the model parameters of the family by the method of maximum likelihood. We prove empirically the flexibility of the proposed model by means of an application to a real data set.

Highlights

Adding parameters to a well-established distribution is a time honored device for obtaining more flexible new families of distributions
Shaw and Buckley [1] pioneered an interesting method of adding a new parameter to an existing distribution that would offer more distributional flexibility. They used the quadratic rank transmutation map (QRTM) in order to generate a flexible family of distributions
A significant amount of work has been attributed towards developing a new transmuted model and subsequently discussing its utilities as enhanced flexibility in modeling various types of real life data, where the parent model does not provide a good fit

Summary

Introduction

Adding parameters to a well-established distribution is a time honored device for obtaining more flexible new families of distributions. Shaw and Buckley [1] pioneered an interesting method of adding a new parameter to an existing distribution that would offer more distributional flexibility. They used the quadratic rank transmutation map (QRTM) in order to generate a flexible family of distributions. The generated family, called the transmuted extended distribution, includes the parent distribution as a special case and gives more flexibility to model various types of data. Elbatal and Aryal [7] explored the transmuted additive Weibull model, which extends the additive Weibull distribution and some other distributions using the QRTM method [1]. This paper aims to fill out this gap in the existing literature and contribute with general properties of the transmuted family

Objectives

Results

Conclusion