Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Review of Parameter Estimation Procedure of Freund Bivariate Exponential Distribution

Freund 이변량 지수분포의 매개변수 추정과정 검토

  • Park, Cheol-Soon (School of Civil, Environmental and Architectural Engineering, College of Engineering, Korea University) ;
  • Yoo, Chul-Sang (School of Civil, Environmental and Architectural Engineering, College of Engineering, Korea University)
  • 박철순 (고려대학교 공과대학 건축사회환경공학부) ;
  • 유철상 (고려대학교 공과대학 건축사회환경공학부)
  • Received : 2011.09.07
  • Accepted : 2011.12.21
  • Published : 2012.02.29
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Abstract

This study reviewed the parameter estimation procedure of the Freund bivariate exponential distribution for the decision of the annual maximum rainfall event. The method of moments was reviewed first, whose results were compared with those from the method of maximum likelihood. Both methods were applied to the hourly rainfall data of the Seoul rain gauge station measured from 1961 to 2010 to select the annual maximum rainfall events, which were also compared each other. The results derived are as follows. First, when applying the method of moments for the parameter estimation, it was found necessary to consider the correlation coefficient between the two variables as well as the mean and variance. Second, the method of maximum likelihood was better to reproduce the mean, but the method of moments was better to reproduce the annual variation of the variance. Third, The annual maximum rainfall events derived were very similar in both cases. Among differently selected annual maximum rainfall events, those with the higher rainfall amount were selected by the method of maximum likelihood, but those with the higher rainfall intensity by the method of moments.

본 연구에서는 연최대치 독립 호우사상의 결정에 사용되는 Freund 이변량 지수분포의 매개변수 추정과정을 구체적으로 검토하였다. 먼저, 모멘트법을 이용하는 경우를 구체적으로 검토하고, 그 결과를 최우도법을 적용한 결과와 비교하였다. 두 방법을 1961~2010년 서울지점의 시강우 자료에 적용하여 연최대치 독립 호우사상을 선정하고, 그 결과를 비교 검토하였다. 이러한 과정을 통해 얻은 결과는 다음과 같다. 첫째, 매개변수 추정방법으로 모멘트법을 적용하는 경우에는 두변량의 평균과 분산뿐만 아니라 상관계수도 고려해 주어야 하는 것으로 나타났다. 둘째, 최우도법은 두변량의 평균에 대한 재현성이 우수하고, 모멘트법은 분산의 경년변동을 잘 나타내는 것으로 나타났다. 셋째, 모멘트법과 최우도법을 통해 선정한 연최대치 독립 호우사상들은 대체로 유사한 것으로 나타났다. 다르게 선정된 호우사상은 최우도법의 경우에는 총 강우량이 큰 것, 모멘트법의 경우에는 강우강도가 큰 것으로 나타났다.

Keywords

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