Gaussian Copula (Bivariate) Distribution

Density, distribution function, and random generation for the (one parameter) bivariate Gaussian copula distribution.

Usage

dbinormcop(x1, x2, rho = 0, log = FALSE)
pbinormcop(q1, q2, rho = 0)
rbinormcop(n, rho = 0)

Arguments

x1, x2, q1, q2

vector of quantiles. The x1 and x2 should be in the interval \((0,1)\). Ditto for q1 and q2.

n

number of observations. Same as rnorm.

rho

the correlation parameter. Should be in the interval \((-1,1)\).

log

Logical. If TRUE then the logarithm is returned.

Value

dbinormcop gives the density, pbinormcop gives the distribution function, and rbinormcop generates random deviates (a two-column matrix).

Author

T. W. Yee

Details

See binormalcop, the VGAM family functions for estimating the parameter by maximum likelihood estimation, for the formula of the cumulative distribution function and other details.

Note

Yettodo: allow x1 and/or x2 to have values 1, and to allow any values for x1 and/or x2 to be outside the unit square.

Examples

if (FALSE)  edge <- 0.01  # A small positive value
N <- 101; x <- seq(edge, 1.0 - edge, len = N); Rho <- 0.7
#> Error: object 'edge' not found
ox <- expand.grid(x, x)
#> Error: object 'x' not found
zedd <- dbinormcop(ox[, 1], ox[, 2], rho = Rho, log = TRUE)
#> Error: object 'ox' not found
contour(x, x, matrix(zedd, N, N), col = "blue", labcex = 1.5)
#> Error: object 'x' not found
zedd <- pbinormcop(ox[, 1], ox[, 2], rho = Rho)
#> Error: object 'ox' not found
contour(x, x, matrix(zedd, N, N), col = "blue", labcex = 1.5)
#> Error: object 'x' not found
 # \dontrun{}