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

Kyungwon Joo,Jun-Haeng Heo,Ju-Young Shin

doi:10.3390/w12041182

Kyungwon Joo, Jun-Haeng Heo + Show 1 more

Open Access

https://doi.org/10.3390/w12041182

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Abstract

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.

Highlights

Hydrological phenomena have multidimensional characteristics; more than one variable is required to be considered in simultaneous analyses of the hydrological phenomena [1].The multivariate probability model accounts for the multidimensional characteristics
For the Seosan station, the parameter estimates by the Maximum Pseudo-Likelihood (MPL) and Inference Function for Margin (IFM) methods are 1.352 and
The parameter estimates of the six employed modified MPL (MMPL) methods range from 1.296 to

Summary

Introduction

Hydrological phenomena have multidimensional characteristics; more than one variable is required to be considered in simultaneous analyses of the hydrological phenomena [1].The multivariate probability model accounts for the multidimensional characteristics. Traditional multivariate probability models that are widely used in the analysis of hydrological data were derived on the basis of univariate probability distribution [2,3,4,5,6]. They assume that random variables follow the distribution model that is utilized in the derivation of multivariate probability distribution model [7]. The copula model has been widely adopted as an alternative to mitigate the limitation of the traditional multivariate probability model in the frequency analysis of multidimensional data.

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Conclusion