The name is absent

24

copulas are created based upon uniform distributed variables. Copulas naturally
have wide applications in statistical modeling.

2.4.1 Different copula functions

In this research, we employ a commonly used two-dimensional copula, Frank (1979)
copula. It is popular because unlike other copulas, Frank copula can model the full
range of association, τ ∈ (—1,1) ∖ {0}. Frank copula is defined as below,

• Frank (1979) copula

fα^u _      _ ι)

H{u. v∙ α) = log {1 + ʌ---------------}, a > 0. a ≠ 1,         (2.19)

'                              a — 1                  '

where и and v represent known uniform variates within the range of 0 and 1. H
represents a copula function. And a is the parameter of a copula.

Several other popular copulas are:

• Independent copula

H(u,υ) = uυ                           (2.20)

• Clayton (1978) copula

H(u, v, a) = (u~^a + v~^a - l)-^1/a, a > 0.               (2.21)

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