Gaussian copula constructor

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

Usage

cgaussian(rho = 0)

Arguments

rho

Correlation parameter (\(-1 < rho < 1\)).

Value

Function of two arguments (u,v) returning log copula density.

The Gaussian copula density is $$ c(u,v;\rho) = \frac{1}{\sqrt{1-\rho^2}} \exp\left\{-\frac{1}{2(1-\rho^2)} (z_1^2 - 2 \rho z_1 z_2 + z_2^2) + \frac{1}{2}(z_1^2 + z_2^2) \right\}, $$ where \(z_1 = \Phi^{-1}(u)\), \(z_2 = \Phi^{-1}(v)\), and \(-1 < \rho < 1\).

See also

cclayton(), cgumbel(), cfrank()

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 = cgaussian(0.5), log = TRUE)
#> [1] -2.818014 -4.809862