Abstract
The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the called Kumaraswamy Pareto distribution, is introduced and studied. The new distribution can have a decreasing and upside-down bathtub failure rate function depending on the values of its parameters. It includes as special sub-models the Pareto and exponentiated Pareto (Gupta et al., 1998) distributions. Some structural properties of the proposed distribution are studied including explicit expressions for the 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 the observed information matrix is derived. A real data set is used to compare the new model with widely known distributions.
Highlights
The Pareto distribution is a very popular model named after a professor of economics: Vilfredo Pareto
The well-known two-parameter Pareto distribution is extended by introducing two extra shape parameters, defining the Kumaraswamy Pareto (Kw-P) distribution having a broader class of hazard rate functions
This is achieved by taking (1) as the baseline cumulative distribution of the generalized class of Kumaraswamy distributions defined by Cordeiro and de Castro (2011)
Summary
The Pareto distribution is a very popular model named after a professor of economics: Vilfredo Pareto. Many beta-type distributions were introduced and studied, see, for example, Barreto-Souza et al (2010) and Silva et al (2010) In this context, we propose an extension of the Pareto distribution based on the family of Kumaraswamy generalized (denoted with the prefix “Kw-G” for short) distributions introduced by Cordeiro and de Castro (2011). We combine the works of Kumaraswamy (1980) and Cordeiro and de Castro (2011) to derive some mathematical properties of a new model, called the Kumaraswamy Pareto (Kw-P) distribution, which stems from the following general construction: if G denotes the baseline cumulative function of a random variable, a generalized class of distributions can be defined by.
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