Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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A Study on Empirical Distribution Function with Unknown Shape Parameter and Extreme Value Weight for Three Parameter Weibull Distribution

3변수 Weibull 분포형의 형상매개변수 및 극치값 가중치를 고려한 EDF 검정에 대한 연구

  • Kim, Taereem (School of Civil and Environmental Engineering, Yonsei Univ.) ;
  • Shin, Hongjoon (School of Civil and Environmental Engineering, Yonsei Univ.) ;
  • Heo, Jun-Haeng (School of Civil and Environmental Engineering, Yonsei Univ.)
  • 김태림 (연세대학교 대학원 토목공학과) ;
  • 신홍준 (연세대학교 대학원 토목공학과) ;
  • 허준행 (연세대학교 사회환경시스템공학부)
  • Received : 2013.02.26
  • Accepted : 2013.03.22
  • Published : 2013.06.30
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Abstract

The most important procedure in frequency analysis is to determine the appropriate probability distribution and to estimate quantiles for a given return period. To perform the frequency analysis, the goodness-of-fit tests should be carried out for judging fitness between obtained data from empirical probability distribution and assumed probability distribution. The previous goodness-of-fit could not consider enough extreme events from the recent climate change. In this study, the critical values of the modified Anderson-Darling test statistics were derived for 3-parameter Weibull distribution and power test was performed to evaluate the performance of the suggested test. Finally, this method was applied to 50 sites in South Korea. The result shows that the power of modified Anderson-Darling test has better than other existing goodness-of-fit tests. Thus, modified Anderson-Darling test will be able to act as a reference of goodness-of-fit test for 3-parameter Weibull model.

적절한 확률분포형을 결정하고 그에 따른 확률수문량을 산정하는 것은 빈도해석에서 가장 중요한 절차이며, 이를 수행하기 위해서는 경험적 확률분포에서 얻어지는 자료와 가정한 확률분포에서 얻어지는 자료의 일치 정도를 판별하는 적합도 검정을 거쳐야 한다. 지금까지 일반적으로 적용된 적합도 검정 방법은 분포형의 전체적인 적합정도를 판별하여 최근의 기상이변으로 인한 극치 사상에 대하여는 충분히 고려하지 못하고 있다. 따라서 본 연구에서는 분포형의 극치 사상에 가중치를 주는 modified Anderson-Darling(AD) 검정 방법을 3변수 Weibull 분포형에 적용하여 검정통계량 한계값과 기각력을 살펴보았으며 이를 실제자료에 적용한 결과, modified AD 검정 방법이 다른 기존의 적합도 검정보다 더 우수한 기각력을 가지고 있음을 확인하였다. 이는 앞으로 3변수 Weibull 분포형을 이용한 극치 수문량 선정에 있어 modified AD 방법이 하나의 기준으로 작용할 수 있을 것이라 판단된다.

Keywords

References

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