| Title |
A Bayesian Approach to Gumbel Mixture Distribution for the Estimation of Parameter and its use to the Rainfall Frequency Analysis |
| Authors |
최홍근(Choi, Hong-Geun) ; 오랑치맥솜야(Uranchimeg, Sumiya) ; 김용탁(Kim, Yong-Tak) ; 권현한(Kwon, Hyun-Han) |
| DOI |
https://doi.org/10.12652/Ksce.2018.38.2.0249 |
| Keywords |
베이지안 기법;빈도해석;혼합 Gumbel 분포형 Bayesian method;BIC;Frequency analysis;Mixed Gumbel distribution |
| Abstract |
More than half of annual rainfall occurs in summer season in Korea due to its climate condition and geographical location. A frequency analysis is mostly adopted for designing hydraulic structure under the such concentrated rainfall condition. Among the various distributions, univariate Gumbel distribution has been routinely used for rainfall frequency analysis in Korea. However, the distributional changes in extreme rainfall have been globally observed including Korea. More specifically, the univariate Gumbel distribution based rainfall frequency analysis is often fail to describe multimodal behaviors which are mainly influenced by distinct climate conditions during the wet season. In this context, we purposed a Gumbel mixture distribution based rainfall frequency analysis with a Bayesian framework, and further the results were compared to that of the univariate. It was found that the proposed model showed better performance in describing underlying distributions, leading to the lower Bayesian information criterion (BIC) values. The mixed Gumbel distribution was more robust for describing the upper tail of the distribution which playes a crucial role in estimating more reliable estimates of design rainfall uncertainty occurred by peak of upper tail than single Gumbel distribution. Therefore, it can be concluded that the mixed Gumbel distribution is more compatible for extreme frequency analysis rainfall data with two or more peaks on its distribution. |