한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제47권2호
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  • Pages.161-170
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  • 2014
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  • 2799-8746(pISSN)
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  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
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표본자료의 왜곡도 영향을 고려한 GEV 분포의 확률도시 상관계수 검정방법 비교 검토

Comparison on Probability Plot Correlation Coefficient Test Considering Skewness of Sample for the GEV Distribution

  • 안현준 (연세대학교 대학원 토목환경공학과) ;
  • 신홍준 (연세대학교 대학원 토목환경공학과) ;
  • 김수영 (연세대학교 대학원 토목환경공학과) ;
  • 허준행 (연세대학교 사회환경공학부 토목환경공학과)
  • Ahn, Hyunjun (School of Civil and Environmental Engineering, Yonsei Univ.) ;
  • Shin, Hongjoon (School of Civil and Environmental Engineering, Yonsei Univ.) ;
  • Kim, Sooyoung (School of Civil and Environmental Engineering, Yonsei Univ.) ;
  • Heo, Jun-Haeng (School of Civil and Environmental Engineering, Yonsei Univ.)
  • 투고 : 2013.12.04
  • 심사 : 2014.01.06
  • 발행 : 2014.02.28
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초록

수공구조물의 설계 시 적절한 확률수문량을 추정하는 것은 매우 중요하며, 이러한 확률수문량을 추정하기 위해서는 표본으로서의 수문자료를 잘 표현할 수 있는 확률분포형을 찾아야 한다. 이와 같이 수문자료에 통계적 특성을 잘 표현할 수 있는 확률분포형을 찾기 위해서 적합도 검정을 실시하며, 적합도 검정 중 하나인 확률도시 상관계수 검정은 비교적 최근에 개발되어 그 사용법이 간단하며 높은 기각능력을 갖는다고 알려져 있다. 본 연구에서는 왜곡도 계수의 영향을 고려할 수 있는 도시위치공식을 이용하여 확률도시 상관계수 검정통계량을 유도하고 그 기각능력을 검토하였으며, 그 결과를 기존에 왜곡도 계수를 고려하지 않은 확률도시 상관계수 검정 방법과 비교해보았다. 그 결과 본 연구에서 유도된 확률도시 상관계수 검정에 의한 기각능력이 기존의 검정 방법들 보다 뛰어났으며, 특히 표본 크기가 작을수록, 발생 분포형이 형상 매개변수를 가질 경우 기각능력이 높게 나타나는 것으로 나타났다.

It is important to estimate an appropriate quantile for design of hydraulic structure. For this purpose, it is necessary to find the appropriate probability distribution which can represent the sample data well. Probability plot correlation coefficient test as one of goodness-of-fit test, is recently developed and has been known as a simple and powerful method. In this study, probability plot correlation coefficient test statistics using the plotting position considering the coefficients of skewness for the GEV distribution is derived, and represented by the regression equation. Monte-Carlo method is also performed to compare the rejection power between each method. As the results, the probability plot correlation coefficient test which is derived in this study is better than the others. In particular, when sample size is small and distribution has the shape parameter, rejection power of probability plot correlation coefficient test considering the coefficients of skewness is bigger than the others.

키워드

참고문헌

  1. Arnell, N.W., Beran, M., and Hosking, J.R.M. (1986). "Unbiased plotting positions for the general extreme value distribution." Journal of Hydrology, Vol. 86, pp. 59-69. https://doi.org/10.1016/0022-1694(86)90006-5
  2. Blom, G. (1958). Statistical estimates and transformed beta variables. John Wiley and Sons, New York.
  3. Chowdhury, J.D., Stedinger, J.R., and Lu, L.H. (1991). "Goodness-of-fit tests for regional generalized extreme value flood distributions." Water Resources Research, Vol. 27, No. 7, pp. 1765-1776. https://doi.org/10.1029/91WR00077
  4. Cunnane, C. (1978). "Unbiased plottoing posiions-A review." Journal of Hydrology, Vol. 37, No. 3/4, pp. 205-222. https://doi.org/10.1016/0022-1694(78)90017-3
  5. Filliben, J.J. (1969). Simple and robust linear estimation of the location parameter of a symmetric distribution. Unpublished Ph.D. dissertation, Princeton university, Princeton, New Jersey.
  6. Filliben, J.J. (1975). "The Probability Plot Correlation Coefficient Test for Normality." Technometrics, Vol. 17, No. 1, pp. 111-117. https://doi.org/10.1080/00401706.1975.10489279
  7. Goel, N.K., and De, M. (1993). "Development of unbiased plotting position formula for General Extreme Value distribution." Stochastic Environmental Research and Risk Assessment, Vol. 7, pp. 1-13.
  8. Gringorten, I.I. (1963). "A plotting rule for extreme probability paper." Journal of Geophysical Research, Vol. 68, No. 3, pp. 813-814. https://doi.org/10.1029/JZ068i003p00813
  9. Gumbel, E.J. (1958). Statistics of Extremes. Columbia University Press, New York, NY.
  10. Guo, S.L. (1990a). "A discussion on unbiased plotting positions for the general extreme value distribution." Journal of Hydrology, Vol. 121, pp. 33-44. https://doi.org/10.1016/0022-1694(90)90223-K
  11. Guo, S.L. (1990b). "Unbiased plotting position formulae for historical floods." Journal of Hydrology, Vol. 121, pp. 45-61. https://doi.org/10.1016/0022-1694(90)90224-L
  12. Hazen, A. (1914). "Storage to be provided in impounding reservoirs for municipal water supply." Transactions American society of Civil Engineers, Vol. 1308, No. 77, pp. 1547-1550.
  13. Heo, J.-H., Kho, Y., Shin, H., Kim, S., and Kim, T. (2008). "Regression equations of probability plot correlation coefficient test statistics from several probability distributions." Journal of Hydrology, Vol. 355, pp. 1-15. https://doi.org/10.1016/j.jhydrol.2008.01.027
  14. Heo, J.-H., Kho, Y.-W., and Kim, K.-D. (2001). "Test statistics derivation and power test for probability plot correlation coefficient goodness of fit test." Journal of Korean Soceity of Civil Engineering, Vol. 21, No. 2-b, pp. 85-92.
  15. In-na, N., and Nguyen, V-T-V. (1989). "An unbiased plotting position formula for the generalized extreme value distribution." Journal of Hydrology, Vol. 106, pp. 193-209. https://doi.org/10.1016/0022-1694(89)90072-3
  16. Jenkinson, A.F. (1955). "The frequency distribution of the annual maximum(or minimum) values of meteorological elements." Quarterly Journal of the Royal Meteorological Society, Vol. 87, pp. 158-171.
  17. Kim, S., Shin, H., Joo, K., and Heo, J.-H. (2012). "Development of plotting position for the general extreme value distribution." Journal of Hydrology, Vol. 475, pp. 259-269. https://doi.org/10.1016/j.jhydrol.2012.09.055
  18. Kimball, B.F. (1946). "Assignment of frequencies to a completely ordered set of sample data." Transaction on the American Geophysical Union, Vol 27. pp. 843-846. https://doi.org/10.1029/TR027i006p00843
  19. Looney, S.W., and Gulledge, T.R. (1985). "Use the correlation coefficient with normal probability plots." The American Statistician, Vol. 39, No. 1, pp. 75-79.
  20. Stedinger, J.R., Vogel, R.M., Foufoula-Georgiou, E. (1993). Frequency analysis of extreme events. Handbook of Hydrology, D.R. Maidment, de., McGraw-Hill, New York, N.Y., pp. 18.24-18.26
  21. Vogel, R.M. (1986). "The probability plot correlation coefficient test for the normal, lognormal, and Gumbel distributional hypotheses."Water Resources Research, Vol. 22, No. 4, pp. 587-590. https://doi.org/10.1029/WR022i004p00587
  22. Vogel, R.M., and McMartin, D.E. (1991). "Probability plot goodness-of-fit and skewness estimation procedures for the Pearson type III distribution."Water Resources Research, Vol. 27, No. 12, pp. 3149-3158. https://doi.org/10.1029/91WR02116