The Kumaraswamy Pareto IV Distribution

Authors

  • Muhammad Hussain Tahir Associate Professor Department of Statistics Baghdad Campus The Islamia University of Bahawalpur Bahawalpur-63100 Pakistan
  • Gauss M. Cordeiro Federal University of Pernambuco
  • Muhammad Mansoor The Islamia University of Bahawalpur
  • Muhammad Zubair Government Degree College Khairpur Tamewali
  • Ayman Alzaatreh Austin Peay State University

DOI:

https://doi.org/10.17713/ajs.v50i5.96

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 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.

Author Biographies

Muhammad Hussain Tahir, Associate Professor Department of Statistics Baghdad Campus The Islamia University of Bahawalpur Bahawalpur-63100 Pakistan

Associate Professor
Department of Statistics
Baghdad Campus
The Islamia University of Bahawalpur
Bahawalpur-63100
Pakistan

Gauss M. Cordeiro, Federal University of Pernambuco

Professor

Department of Statistics,

Federal University of Pernambuco,
50740-540, Recife, PE, Brazil.

Ayman Alzaatreh, Austin Peay State University

Assiatant Professor, Department of Mathematics and Statistics, Austin Peay State University, Clarksville, USA

References

Reviewers (Proposed)

José María Sarabia

Department of Economics, University of Cantabria,

Avda. de los Castros s/n 39005-Santander. SPAIN

Email: sarabiaj@unican.es

Abdus Saboor

Department of Mathematics, Kohat University of Science & Technology, Kohat, Pakistan

Email addresses: saboorhangu@gmail.com; dr.abdussaboor@kust.edu.pk

-9023914

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

Email: hnbakouch@yahoo.com

Broderick O. Oluyede

Department of Mathematical, Sciences Georgia Southern University, Statesboro, GA 30460, USA

Email: boluyede@georgiasouthern.edu

Downloads

Published

2021-08-25

How to Cite

Tahir, M. H., Cordeiro, G. M., Mansoor, M., Zubair, M., & Alzaatreh, A. (2021). The Kumaraswamy Pareto IV Distribution. Austrian Journal of Statistics, 50(5), 1–22. https://doi.org/10.17713/ajs.v50i5.96