cgumbel: Gumbel copula constructors

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

Gumbel copula constructors

Description

Construct functions that compute either the log density or the CDF of the bivariate Gumbel copula, intended for use with dcopula.

Usage

cgumbel(theta)

Cgumbel(theta)

Arguments

theta

Dependence parameter (\theta >= 1).

Details

The Gumbel copula density

c(u,v;\theta) = \exp\Big[-\big((-\log u)^\theta + (-\log v)^\theta\big)^{1/\theta}\Big] \cdot h(u,v;\theta),

where h(u,v;\theta) contains the derivative terms ensuring the function is a density.

Value

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

See Also

cgaussian(), cclayton(), cfrank()

Examples

x <- c(0.5, 1); y <- c(0.2, 0.4)
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 = cgumbel(1.5), log = TRUE)

# CDF version (for discrete copulas)
Cgumbel(1.5)(0.5, 0.4)

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