The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A Bayesian Prediction of the Generalized Pareto Model

일반화 파레토 모형에서의 베이지안 예측

  • Huh, Pan (Department of Statistics, Kyungpook National University) ;
  • Sohn, Joong Kweon (Department of Statistics, Kyungpook National University)
  • 판허 (경북대학교 통계학과) ;
  • 손중권 (경북대학교 통계학과)
  • Received : 2014.08.29
  • Accepted : 2014.10.22
  • Published : 2014.12.31
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Abstract

Rainfall weather patterns have changed due to global warming and sudden heavy rainfalls have become more frequent. Economic loss due to heavy rainfall has increased. We study the generalized Pareto distribution for modelling rainfall in Seoul based on data from 1973 to 2008. We use several priors including Jeffrey's noninformative prior and Gibbs sampling method to derive Bayesian posterior predictive distributions. The probability of heavy rainfall has increased over the last ten years based on estimated posterior predictive distribution.

기후 온난화의 한 현상으로 받아들여지는 집중호우로 인한 관심이 늘어난 만큼 강우량에 대한 예측 모형이 필요하다. 이러 환경 문제를 다룰 때, 모형을 설정하는 방법 중에 하나로 일반화 파레토 모형을 활용하는 연구가 이루어지고 있다. 본 논문에서는 서울특별시에 대한 1973년부터 2011년까지 매 7월 일별강우량 자료를 가지고 일반화 파레토 모형을 사용하여 강우량의 임계값(70mm) 이상의 분포가 어떻게 되는지 연구한다. 모수의 사전분포는 감마분포랑 역감마분포를 정의하고, 또는 제프리의 정보가 없는 사전분포를 두고, 깁스 표본방법을 통해 베이지안 사후예측분포를 구하고 얻어진 결과를 비교해 본다.

Keywords

References

  1. Castillo, E. and Hadi, A. S. (1997). Fitting the generalized Pareto distribution to data, Journal of the American Statistical Association, 92, 1609-1620. https://doi.org/10.1080/01621459.1997.10473683
  2. Castillo, J. and Daoudib J. (2008). Estimation of the generalized Pareto distribution, Statistics & Probability Letters, In Press.
  3. Davidson, A. C. (1984). Modeling excesses over high threshold with an application, In: J. Tiago de Oliveria (ed.), Statistical Extremes and Applications, Reidel, Dordrech, 416-482.
  4. Fitzgerald, D. L. (1989). Single station and regional analysis of daily rainfall extremes, Stochastic Hydrology and Hydraulics, 3(4), 281-292. https://doi.org/10.1007/BF01543461
  5. Gelfand, A. E., Hills, S. E., Racine-Poon, A. and Smith, A. F. M. (1990). Illustration of Bayesian inference in normal data models using Gibbs sampling, Journal of the American Statistical Association, 85, 972-985. https://doi.org/10.1080/01621459.1990.10474968
  6. Li, Y., Cai, W. and Campbell, E. P. (2005). Statistical modeling of extreme rainfall in southwest Western Australia. Journal of Climate, 18.
  7. National Emergency Agency (2011). 2011 재해연보, 소방방재청 복구지원과.
  8. Pareto, V. (1897). Cours d'economic politique, Lausanee and Paris; Range and Ci.
  9. Pickands, J. (1975). Statistical inference using extreme order statistics, The Annals of Statistics,3, 119-131. https://doi.org/10.1214/aos/1176343003
  10. Van Montfort, M. A. J. and Witter, J. V. (1986). The generalized Pareto distribution applied to rainfall depths, Hydrological Sciences Journal, 31, 151-162. https://doi.org/10.1080/02626668609491037