The Burr X Pareto Distribution: Properties, Applications and VaR Estimation

Mustafa Ç. Korkmaz, Emrah Altun, Haitham M. Yousof, Ahmed Z. Afify and Saralees Nadarajah
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Mustafa Ç. Korkmaz: Department of Measurement and Evaluation, Artvin Çoruh University, Artvin 08000, Turkey
Emrah Altun: Department of Statistics, Hacettepe University, Ankara 06800, Turkey
Haitham M. Yousof: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt
Ahmed Z. Afify: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt
Saralees Nadarajah: School of Mathematics, University of Manchester, Manchester M13 9PL, UK

JRFM, 2017, vol. 11, issue 1, 1-16

Abstract: In this paper, a new three-parameter Pareto distribution is introduced and studied. We discuss various mathematical and statistical properties of the new model. Some estimation methods of the model parameters are performed. Moreover, the peaks-over-threshold method is used to estimate Value-at-Risk (VaR) by means of the proposed distribution. We compare the distribution with a few other models to show its versatility in modelling data with heavy tails. VaR estimation with the Burr X Pareto distribution is presented using time series data, and the new model could be considered as an alternative VaR model against the generalized Pareto model for financial institutions.

Keywords: Burr X distribution; Pareto distribution; maximum likelihood estimation; heavy tail distribution; value-at-risk (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2017
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