Abstract
Copulas have recently emerged as practical methods for multivari ate modeling. To our knowledge, only a limited amount of work has been done to apply copula-based modeling in context analysis. In this study, we generalized Clayton copula under the appropriate weighted function. In some examples, bivariate distributions by using the weighted Clayton cop ula are generalized. Also the properties of generalized Clayton copula are provided. The Clayton copula and weighted Clayton model cannot be used for negative dependence. These have been used to study left tail depen dence. This property is stronger in weighted Clayton model with respect to ordinary Clayton copula. It will also be shown that the generalized Clayton copula is suitable for the probable modeling of the hydrology data.
Highlights
There exists plenty of evidence for dependence among variables, ignoring the dependence structure solely for mathematical simplicity
; we propose a new family of the generalized Clayton copula by using weighted distribution function of type II Pareto distribution
We proposed a new family of copulas, namely, the generalizing Clayton family that is generated by weighted distribution function and we obtained a generalized d-dimensional (Multivariate) Clayton copula
Summary
There exists plenty of evidence for dependence among variables, ignoring the dependence structure solely for mathematical simplicity. Where X and Y are identical type II Pareto distributions F(x) = (1 + x)−β and F(y) = (1 + y)−β respectively (Genest and Rivest, 1993) This assay aims at extending family copula of Clayton by considering the weighted function. An important advantage of using weighted copulas is that the marginal behavior and the dependence structure can be studied separately. This study applies the weighted copula modeling in design hydrology analysis, with most applications in bivariate analysis, for example, the dependence modeled between storm intensity and duration, peak intensity and depth, depth and duration, and peak intensity and duration.
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