Open AccessThe Kumaraswamy Pareto IV Distribution
Author(s) -
M. H. Tahir,
Gauss M. Cordeiro,
Muhammad Mansoor,
Muhammad Zubair,
Ayman Alzaatreh
Publication year - 2021
Publication title -
österreichische zeitschrift für statistik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.342
H-Index - 9
ISSN - 1026-597X
DOI - 10.17713/ajs.v50i5.96
Subject(s) - mathematics , pareto principle , pareto interpolation , quantile function , lomax distribution , pareto distribution , generalized pareto distribution , bathtub , bonferroni correction , probability density function , statistics , order statistic , lorenz curve , moment generating function , mathematical analysis , gini coefficient , extreme value theory , archaeology , economic inequality , inequality , history
We introduce a new model named the Kumaraswamy Pareto IV distribution which extends the Pareto and Pareto IV distributions. The density function is very flexible and can be left-skewed, right-skewed and symmetrical shapes. It hasincreasing, decreasing, upside-down bathtub, bathtub, J and reversed-J shaped hazard rate shapes. Various structural properties are derived including explicit expressions for the quantile function, ordinary and incomplete moments,Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments and generating function. We provide the density function of the order statistics and their moments. The Renyi and q entropies are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of three real-life data sets. In fact, our proposed model provides a better fit to these data than the gamma-Pareto IV, gamma-Pareto, beta-Pareto,exponentiated Pareto and Pareto IV models.