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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mustafa Ç. Korkmaz & Emrah Altun & Haitham M. Yousof & Ahmed Z. Afify & Saralees Nadarajah, 2017. "The Burr X Pareto Distribution: Properties, Applications and VaR Estimation," JRFM, MDPI, vol. 11(1), pages 1-16, December.
    • Handle: RePEc:gam:jjrfmx:v:11:y:2017:i:1:p:1-:d:123862
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    References listed on IDEAS

    as
    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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