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Clayton copula constructors

cclayton.Rd

Construct a function that computes the log density or CDF of the bivariate Clayton copula, intended to be used with dcopula.

Usage

cclayton(theta)

Cclayton(theta)

Arguments

theta

Positive dependence parameter (\(\theta > 0\)).

Value

A function of two arguments (u,v) returning log copula density (cclayton) or copula CDF (Cclayton).

Details

The Clayton copula density is $$ c(u,v;\theta) = (1+\theta) (uv)^{-(1+\theta)} \left( u^{-\theta} + v^{-\theta} - 1 \right)^{-(2\theta+1)/\theta}, \quad \theta > 0. $$

See also

cgaussian(), cgumbel(), cfrank()

Examples

x <- c(0.5, 1); y <- c(0.2, 0.8)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dbeta(y, 2, 1, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pbeta(y, 2, 1)
dcopula(d1, d2, p1, p2, copula = cclayton(2), log = TRUE)
#> [1] -3.8093660 -0.1671136

# CDF version (for discrete copulas)
Cclayton(1.5)(0.5, 0.4)
#> [1] 0.3104447