IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1211.0130.html
   My bibliography  Save this paper

The full-tails gamma distribution applied to model extreme values

Author

Listed:
  • Joan del castillo
  • Jalila Daoudi
  • Isabel Serra

Abstract

In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory. The results are useful to certain phenomena that are fitted by the Pareto distribution but, at the same time, they present a deviation from this law for very large values. Two examples of data analysis with the new model are provided. The first one is on the influence of climate variability on the occurrence of tropical cyclones. The second one on the analysis of aggregate loss distributions associated to operational risk management.

Suggested Citation

  • Joan del castillo & Jalila Daoudi & Isabel Serra, 2012. "The full-tails gamma distribution applied to model extreme values," Papers 1211.0130, arXiv.org.
    • Handle: RePEc:arx:papers:1211.0130
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1211.0130
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    2. Degen, Matthias & Embrechts, Paul & Lambrigger, Dominik D., 2007. "The Quantitative Modeling of Operational Risk: Between G-and-H and EVT," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 265-291, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cristiano Villa, 2017. "Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 95-118, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lu, Zhaoyang, 2011. "Modeling the yearly Value-at-Risk for operational risk in Chinese commercial banks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 604-616.
    2. Pavel V. Shevchenko, 2010. "Implementing loss distribution approach for operational risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 277-307, May.
    3. Udo Milkau & Jürgen Bott, 2018. "Active Management of Operational Risk in the Regimes of the “Unknown”: What Can Machine Learning or Heuristics Deliver?," Risks, MDPI, vol. 6(2), pages 1-16, April.
    4. Dominik D. Lambrigger & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "The Quantification of Operational Risk using Internal Data, Relevant External Data and Expert Opinions," Papers 0904.1361, arXiv.org.
    5. Embrechts, Paul & Neslehová, Johanna & Wüthrich, Mario V., 2009. "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 164-169, April.
    6. José Francisco Martínez-Sánchez & Francisco Venegas-Martínez, 2013. "Riesgo operacional en la banca trasnacional: un enfoque bayesiano," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 31-72, May.
    7. Francisco Venegas-Martínez & José Francisco Martínez-Sánchez & María Teresa V. Martínez-Palacios, 2016. "An analysis on operational risk in international banking: A Bayesian approach (2007–2011)," Estudios Gerenciales, Universidad Icesi, vol. 32(140), pages 208-220, September.
    8. Stefan Mittnik & Sandra Paterlini & Tina Yener, 2011. "Operational–risk Dependencies and the Determination of Risk Capital," Center for Economic Research (RECent) 070, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    9. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    10. M. Naresh Kumar & V. Sree Hari Rao, 2015. "A New Methodology for Estimating Internal Credit Risk and Bankruptcy Prediction under Basel II Regime," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 83-102, June.
    11. Robert Jarrow & Jeff Oxman & Yildiray Yildirim, 2010. "The cost of operational risk loss insurance," Review of Derivatives Research, Springer, vol. 13(3), pages 273-295, October.
    12. J. Christopher Westland, 2015. "Economics of eBay’s buyer protection plan," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 1(1), pages 1-20, December.
    13. S�verine Plunus & Georges Hübner & Jean-Philippe Peters, 2012. "Measuring operational risk in financial institutions," Applied Financial Economics, Taylor & Francis Journals, vol. 22(18), pages 1553-1569, September.
    14. Ikefuji, Masako & Laeven, Roger J.A. & Magnus, Jan R. & Muris, Chris, 2020. "Expected utility and catastrophic risk in a stochastic economy–climate model," Journal of Econometrics, Elsevier, vol. 214(1), pages 110-129.
    15. Ghosh, Souvik & Resnick, Sidney, 2010. "A discussion on mean excess plots," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1492-1517, August.
    16. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    17. Giuseppe Galloppo & Alessandro Rogora, 2011. "What Has Worked In Operational Risk?," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 5(3), pages 1-17.
    18. Pflug Georg Ch. & Schaller Peter, 2009. "A note on pivotal Value-at-Risk estimates," Statistics & Risk Modeling, De Gruyter, vol. 27(3), pages 201-209, December.
    19. Stefan Aulbach & Verena Bayer & Michael Falk, 2012. "A multivariate piecing-together approach with an application to operational loss data," Papers 1205.1617, arXiv.org.
    20. Mainik Georg & Rüschendorf Ludger, 2012. "Ordering of multivariate risk models with respect to extreme portfolio losses," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 73-106, March.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1211.0130. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.