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

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.

A Copula-Based Approach for Modelling the Dependence between Inflation and Exchange Rate in Kenya

“…Any fitting method of a univariate probability distribution is used to first fit the marginal distributions for each random variable. The copula parameter is calculated in the second stage using the maximum likelihood approach [19]. The maximum likelihood method, a parametric approach, is used in the first stage to estimate the copula's parameters.…”

“…The maximum likelihood method, a parametric approach, is used in the first stage to estimate the copula's parameters. However, using order statistics from each sample of data, a nonparametric approach, the CDF (Non-Exceedance Probabilities) from the marginal distribution are estimated [19]. The maximum pseudo-likelihood method combines parametric and nonparametric approaches.…”