An Alternative Study of the Determination of the Threshold for the Generalized Pareto Distribution

일반화 파레토 분포에서 임계치 결정에 대한 대안적 연구

Yoon, Jeong-Yoen;Cho, Jae-Beom;Jun, Byoung-Cheol

  • Received : 20101200
  • Accepted : 20110700
  • Published : 2011.10.31


In practice, thresholds are determined by the two subjective assessment methods in a generalized pareto distribution of mean extreme function(MEF-graph) or Hill-graph. To remedy the problem of subjectiveness of these methods, we propose an alternative method to determine the threshold based on the robust statistics. We compared the MEF-graph, Hill-graph and our method through VaRs on the Korean stock market data from January 5, 1987 to August 3, 2009. As a result, the VaR based on the proposed method is not much different from the existing methods, and the standard deviation of VaR for our method was the smallest. The results show that our method can be a promising alternative to determine thresholds of the generalized pareto distributions.


Generalized pareto distribution;threshold;MEF-graph;Hill-graph;robust estimation;VaR


  1. 송문섭 (1996). <로버스트 통계>, 자유아카데미, 서울.
  2. 윤평식, 김철중 (2000). <금융기관 시장위험관리>, 한국금융연수원, 서울.
  3. Beirlant, J., Teugels, J. L. T. and Vynckier, P. (1996). Practical Analysis of Extreme Values, Leuven University Press, Leuven.
  4. Journal of the American Statistical Association, 92, 1609-1620.
  5. Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer, New York.
  6. Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological elements, Quarterly Journal of the Royal Meteorological Society, 81, 158-171.
  7. McNeil, A. J. (1999). Extreme value theory for risk managers, In Internal Modelling and CAD II, pp. 93-113, Risk books.
  8. Selcuk, F. and Ramazan, G. (2001). Overnight Borrowing, Interest Rates and Extreme Value Theory, Departmental Working Papers 0103, Department of Economics, Bilkent University,