Parameter estimation of copula functions using an optimization-based method

Application of the copulas can be useful for the accurate multivariate frequency analysis of hydrological phenomena. There are many copula functions and some methods were proposed for estimating the copula parameters. Since the copula functions are mathematically complicated, estimating of the copul...

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Bibliographic Details
Published in:Theoretical and applied climatology 2017-07, Vol.129 (1-2), p.21-32
Main Authors: Abdi, Amin, Hassanzadeh, Yousef, Talatahari, Siamak, Fakheri-Fard, Ahmad, Mirabbasi, Rasoul
Format: Article
Language:English
Subjects:
Analysis
Aquatic Pollution
Atmospheric Protection/Air Quality Control/Air Pollution
Atmospheric Sciences
Climate science
Climatology
Drought
Drought characteristics
Earth and Environmental Science
Earth Sciences
Estimation
Frequency analysis
Functions (mathematics)
Gaging
Hydrologic analysis
Hydrology
Inference
Mathematical analysis
Method of moments
Methods
Optimization
Optimization techniques
Original Paper
Parameter estimation
Parameters
Probability distribution
Probability distributions
Probability theory
Waste Water Technology
Water Management
Water Pollution Control
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Summary:Application of the copulas can be useful for the accurate multivariate frequency analysis of hydrological phenomena. There are many copula functions and some methods were proposed for estimating the copula parameters. Since the copula functions are mathematically complicated, estimating of the copula parameter is an effortful work. In the present study, an optimization-based method (OBM) is proposed to obtain the parameters of copulas. The usefulness of the proposed method is illustrated on drought events. For this purpose, three commonly used copulas of Archimedean family, namely, Clayton, Frank, and Gumbel copulas are used to construct the joint probability distribution of drought characteristics of 60 gauging sites located in East-Azarbaijan province, Iran. The performance of OBM was compared with two conventional methods, namely, method of moments and inference function for margins. The results illustrate the supremacy of the OBM to estimate the copula parameters compared to the other considered methods.
ISSN:0177-798X
1434-4483
DOI:10.1007/s00704-016-1757-2