cfrank: Frank copula constructor

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

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)

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.

Value

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

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)

RTMBdist documentation built on April 1, 2026, 5:07 p.m.