Statistical Estimation of Extreme Values in the Mixture Distributions
- Authors
- 최양호; 곽원선; 구혜인; 안재윤
- Issue Date
- Dec-2014
- Publisher
- 한국리스크관리학회
- Keywords
- Mixture distribution; Extreme behavior; Precipitation; Generalized extreme distribution; Generalized Pareto distribution; 혼합분포; 극단치; 강수량; 일반 극단치 분포; 일반 파레토 분포
- Citation
- 리스크관리연구, v.25, no.3, pp.31 - 56
- Indexed
- KCI
- Journal Title
- 리스크관리연구
- Volume
- 25
- Number
- 3
- Start Page
- 31
- End Page
- 56
- URI
- https://scholarworks.bwise.kr/erica/handle/2021.sw.erica/24216
- DOI
- 10.21480/tjrm.25.3.201412.002
- ISSN
- 1229-103X
- Abstract
- In this paper, we address possible bias issues in quantile estimation using generalized extreme value distribution (GEV). We first provide two examples, one from a Fréchet-Gumbel mixture distribution and the other from a Gumbel-Gumbel mixture distribution, which explain theoretical asymptotic convergence of extreme value estimators to GEV in cases of mixture distributions. However, through a simple example, we show that the convergence rate can be arbitrarily slow for some cases, and explain that slow convergence rates can create bias in actual statistical estimations of the quantile of extreme values. To reduce the bias in quantile estimation of extreme values, we briefly mention that (modified) GPD method can be effective, depending on the data size available. Finally, actual data on the precipitation in Seoul are analyzed using both the GEV and GPD method.
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