Application of PSO Method for Archimedean Copula Parameter Estimation in Flood (Rain) and Tide Joint Distribution Analysis

Abstract Copulas are appropriate tools in drought frequency analysis. However, uncertainties originating from copulas in such frequency analysis have not received significant consideration. This study aims to develop a drought severity-areal extent-frequency (SAF) curve with copula theory and to evaluate the uncertainties in the curve. Three uncertainty sources are considered: different copula functions, copula parameter estimations, and copula input data. A case study in Heihe River basin in China is used as an example to illustrate the proposed approach. Results show that: (1) the dependence structure of drought severity and areal extent can be modeled well by Gumbel; Clayton and Frank depart the most from Gumbel in estimating drought SAF curves; (2) both copula parameter estimation and copula input data contribute to the uncertainties of SAF curves; uncertainty ranges associated with copula input data present wider than those associated with parameter estimations; (3) with the conditional probability decreasing, the differences in the curves derived from different copulas are increasing, and uncertainty ranges of the curves caused by copula parameter estimation and copula input data are also increasing. These results highlight the importance of uncertainty analysis of copula application, given that most studies in hydrology and climatology use copulas for extreme analysis.

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ANALISIS HUBUNGAN PRODUKSI PADI DAN INDIKATOR ENSO DI KABUPATEN TABANAN DENGAN PENDEKATAN COPULA

E-Jurnal Matematika ◽

10.24843/mtk.2016.v05.i04.p136 ◽

2016 ◽

Vol 5 (4) ◽

pp. 164

Author(s):

LUH GEDE UDAYANI ◽

I WAYAN SUMARJAYA ◽

MADE SUSILAWATI

Keyword(s):

Joint Distribution ◽

Southern Oscillation ◽

Pearson Correlation ◽

Archimedean Copula ◽

Model Structure ◽

Wide Range ◽

Frank Copula ◽

Probability And Statistics ◽

Dependency Model ◽

Dependence Relationship

Dependence relationship between two or more variables is an issue that is often studied in the science of probability and statistics. Pearson correlation is often the easiest option to measure dependencies between variables. It is well known, that Pearson correlation assumes that the variable under study must be normally distributed. However, in reality this is not the case; for example, data in fields such as climatology and meteorology, insurance, and financial. Copula is a tool that can be used to model the joint distribution because it does not require the assumption of normality of the data so that it is resilient against a wide range of data. In this study, we discussed the application of copula in modeling the structure of dependencies between two variables: the production of rice and El-Nino Southern Oscillation (ENSO) indicator per period in Tabanan Regency. The best dependency model structure is given by the Frank copula of the Archimedean copula family with estimation parameter, ? = 2,817 and the loglikelihood value of 3,47.

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