Abstract
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.
Highlights
The Pareto distribution and its generalizations are tractable statistical models for scientists, economists and engineers
We propose an extension of the Pareto-IV model called the Kumaraswamy Pareto-IV (“Kumaraswamy Pareto IV distribution (KwPIV)” for short) distribution based on equations (5) and (6)
We propose a new five-parameter Kumaraswamy Pareto IV distribution (KwPIV) distribution
Summary
The Pareto distribution and its generalizations are tractable statistical models for scientists, economists and engineers. A very generalized form of the Pareto model is the four-parameter Pareto IV (PIV) distribution defined by the cumulative distribution function (cdf). Where g(x) = dG(x)/dx and a > 0 and b > 0 are two extra shape parameters whose role are to govern skewness and tail weights In this context, we propose an extension of the Pareto-IV model called the Kumaraswamy Pareto-IV (“KwPIV” for short) distribution based on equations (5) and (6).
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