RTMBdist (version 1.0.1)

cfrank: Frank copula constructor

Description

Returns a function computing the log density of the bivariate Frank copula, intended to be used with dcopula.

Usage

cfrank(theta)
Cfrank(theta)

Value

A function of two arguments (u, v) returning either the log copula density (cfrank) or the copula CDF (Cfrank).

Arguments

theta

Dependence parameter (\(\theta \neq 0\)).

Details

The Frank copula density is $$ c(u,v;\theta) = \frac{\theta (1-e^{-\theta}) e^{-\theta(u+v)}} {\left[(e^{-\theta u}-1)(e^{-\theta v}-1) + (1 - e^{-\theta}) \right]^2}, \quad \theta \ne 0. $$

See Also

cgaussian(), cclayton(), cgumbel()

Examples

x <- c(0.5, 1); y <- c(1, 2)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dexp(y, 2, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pexp(y, 2)
dcopula(d1, d2, p1, p2, copula = cfrank(2), log = TRUE)