The Kumaraswamy transmuted Pareto distribution

Hongwei Long,Alfred A Akinsete,Gokarna Aryal,Sher B Chhetri

doi:10.1186/s40488-017-0065-4

Abstract

In this work, a new five-parameter Kumaraswamy transmuted Pareto (KwTP) distribution is introduced and studied. We discuss various mathematical and statistical properties of the distribution including obtaining expressions for the moments, quantiles, mean deviations, skewness, kurtosis, reliability and order statistics. The estimation of the model parameters is performed by the method of maximum likelihood. We compare the distribution with few other distributions to show its versatility in modeling data with heavy tail.

Highlights

Furtherance to the work by Eugene et al (2002), who proposed and defined the betagenerated class of distributions for a continuous random variable, derived from the logit of the beta random variable, many statistical distributions have been proposed and studied by numerous authors
According to Eugene et al (2002), suppose X is a random variable with cumulative distribution function (CDF) F(x), the CDF for the beta-generated family is obtained by applying the inverse probability transformation to the beta density function
13 Conclusion We have proposed in this article, a new distribution that is being referred to as the Kumaraswamy transmuted Pareto (KwTP)

Summary

Introduction

Furtherance to the work by Eugene et al (2002), who proposed and defined the betagenerated class of distributions for a continuous random variable, derived from the logit of the beta random variable, many statistical distributions have been proposed and studied by numerous authors. Using the quadratic rank transmutation map, Merovci and Puka (2014) generalized the Pareto distribution to obtain what the authors called the transmuted Pareto distribution They provided a comprehensive description of the mathematical properties of the distribution and its application in modeling real life data. A random variable X is said to have the transmuted Pareto distribution with scale parameter θ > 0, shape parameter α > 0, and the transmuted parameter λ (|λ| ≤ 1), if its PDF is given by αθα θα g(x; α, θ , λ) = xα+1 1 − λ + 2λ x , where θ is the (necessarily positive) minimum possible value of X. When a = b = 1, KwTP reduces to the transmuted Pareto distribution by Merovci and Puka (2014) with PDF αθα θα f (x; α, θ , λ) = xα+1 1 − λ + 2λ x.

Quantile function

Moment functions

10 Parameter estimation

13 Conclusion