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2020 Vol.13, Issue 1

Original Article

Derivation of Probability Plot Correlation Coefficient Test Statistics and Regression Equation for the GEV Model based on L-moments

L-모멘트 법 기반의 GEV 모형을 위한 확률도시 상관계수 검정 통계량 유도 및 회귀식 산정

Hyunjun Ahn1
,
Changsam Jeong2
,
Jun-Haeng Heo3*
안 현준1
,
정 창삼2
,
허 준행3*
1Ph.D Candidate, Civil and Environmental Engineering, Yonsei University
2Professor, Civil and Environmental Engineering, Induk University
3Professor, Civil and Environmental Engineering, Yonsei University
1연세대학교 대학원 토목환경공학과 통합과정
2인덕대학교 토목환경공학과 부교수
3연세대학교 사회환경공학부 토목환경공학과 교수
*Corresponding Author
31 March 2020. pp. 1-11
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Abstract

One of the important problem in statistical hydrology is to estimate the appropriated probability distribution for a given sample data. For the problem, a goodness-of-fit test is conducted based on the similarity between estimated probability distribution and assumed theoretical probability distribution. Probability plot correlation coefficient test (PPCC) is one of the goodness-of-fit test method. PPCC has high rejection power and its application is simple. In this study, test statistics of PPCC were derived for generalized extreme value distribution (GEV) models based on L-moments and these statistics were suggested by the multiple and nonlinear regression equations for its usability. To review the rejection power of the newly proposed method in this study, Monte Carlo simulation was performed with other goodness-of-fit tests including the existing PPCC test. The results showed that PPCC-A test which is proposed in this study demonstrated better rejection power than other methods, including the existing PPCC test. It is expected that the new method will be helpful to estimate the appropriate probability distribution model.

Keywords
Goodness-of-fit test
PPCC
GEV
L-moment
Monte Carlo simulation

수문 통계 분야에서 관측된 자료를 대표할 수 있는 확률분포 모형을 추정하는 일은 매우 중요한 문제이다. 이를 위해 표본 자료로부터 추정되는 확률분포 모형과 가정된 이론적 확률분포 모형의 일치 정도를 통해 적합도 검정을 수행한다. 확률 도시 상관계수 검정(PPCC)은 적합도 검정 방법 중 하나로 적용 방법이 간편하면서도 높은 기각력을 가지고 있다. 본 연구에서는 L-모멘트 법 기반의 generalized extreme value(GEV) 분포 모형을 위한 PPCC의 검정 통계량을 유도하고 이를 다변량 비선형 형태의 회귀식으로 제시하였다. 새롭게 제시된 방법의 기각력을 검토하고자 기존의 적합도 검정 방법들과 모의실험을 수행하였으며 그 결과 본 연구에서 제시된 PPCC-A 검정 방법이 기존의 PPCC 검정을 비롯한 다른 적합도 검정 방법보다 우수한 기각력을 보이는 것으로 나타났다. 이를 통해 표본 자료를 좀 더 정확하게 대표할 수 있는 확률분포 모형을 구축하는 데 도움이 될 것으로 기대된다.

키워드
적합도 검정
확률 도시 상관계수 검정
GEV 분포
L-모멘트
몬테카를로 모의실험
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Korean References Translated from the English

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2
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3
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Information
  • Publisher :Korean Society of Disaster and Security
  • Publisher(Ko) :한국방재안전학회
  • Journal Title :Journal of Korean Society of Disaster and Security
  • Journal Title(Ko) :한국방재안전학회 논문집
  • Volume : 13
  • No :1
  • Pages :1-11
  • Received Date : 2020-02-07
  • Revised Date : 2020-02-24
  • Accepted Date : 2020-02-28
  • DOI :https://doi.org/10.21729/ksds.2020.13.1.1
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