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Open AccessArticle

Modified Maximum Pseudo Likelihood Method of Copula Parameter Estimation for Skewed Hydrometeorological Data

1
Department of Civil and Environmental Engineering, Yonsei University, Seoul 03722, Korea
2
Applied Meteorology Research Division, National Institute of Meteorological Sciences, Seogwipo-si 63568, Korea
*
Author to whom correspondence should be addressed.
Water 2020, 12(4), 1182; https://doi.org/10.3390/w12041182
Received: 10 March 2020 / Revised: 7 April 2020 / Accepted: 14 April 2020 / Published: 20 April 2020
(This article belongs to the Section Hydrology and Hydrogeology)
For multivariate frequency analysis of hydrometeorological data, the copula model is commonly used to construct joint probability distribution due to its flexibility and simplicity. The Maximum Pseudo-Likelihood (MPL) method is one of the most widely used methods for fitting a copula model. The MPL method was derived from the Weibull plotting position formula assuming a uniform distribution. Because extreme hydrometeorological data are often positively skewed, capacity of the MPL method may not be fully utilized. This study proposes the modified MPL (MMPL) method to improve the MPL method by taking into consideration the skewness of the data. In the MMPL method, the Weibull plotting position formula in the original MPL method is replaced with the formulas which can consider the skewness of the data. The Monte-Carlo simulation has been performed under various conditions in order to assess the performance of the proposed method with the Gumbel copula model. The proposed MMPL method provides more precise parameter estimates than does the MPL method for positively skewed hydrometeorological data based on the simulation results. The MMPL method would be a better alternative for fitting the copula model to the skewed data sets. Additionally, applications of the MMPL methods were performed on the two weather stations (Seosan and Yeongwol) in South Korea. View Full-Text
Keywords: parameter estimation of copula model; Gumbel copula; maximum pseudo-likelihood; modified maximum pseudo-likelihood; inference function for margin method parameter estimation of copula model; Gumbel copula; maximum pseudo-likelihood; modified maximum pseudo-likelihood; inference function for margin method
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Joo, K.; Shin, J.-Y.; Heo, J.-H. Modified Maximum Pseudo Likelihood Method of Copula Parameter Estimation for Skewed Hydrometeorological Data. Water 2020, 12, 1182.

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