The Kumaraswamy Pareto IV Distribution
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 has
increasing, 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.
José María Sarabia
Department of Economics, University of Cantabria,
Avda. de los Castros s/n 39005-Santander. SPAIN
Department of Mathematics, Kohat University of Science & Technology, Kohat, Pakistan
Email addresses: firstname.lastname@example.org; email@example.com
Victor H. Lachos
Departamento de Estatística
Instituto de Matemática e Estatística e Computação Científica, IMECC-UNICAMP.
Rua Sergio Buarque de Holanda, 651 Cidade Universitária- Barão Geraldo
CEP: 13083-859 Campinas, SP, Brasil
Email: hlachos@ ime.unicamp.br
Hassan S. Bakouch
Statistics Department, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia
Broderick O. Oluyede
Department of Mathematical, Sciences Georgia Southern University, Statesboro, GA 30460, USA
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