Binormcop {VGAM} | R Documentation

## Gaussian Copula (Bivariate) Distribution

### Description

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.

### 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.

### Value

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

### 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.

### Author(s)

T. W. Yee

### See Also

`binormalcop`, `binormal`.

### Examples

    ## Not run:  edge <- 0.01  # A small positive value
    N <- 101; x <- seq(edge, 1.0 - edge, len = N); Rho <- 0.7
    ox <- expand.grid(x, x)
    zedd <- dbinormcop(ox[, 1], ox[, 2], rho = Rho, log = TRUE)
    contour(x, x, matrix(zedd, N, N), col = "blue", labcex = 1.5)
    zedd <- pbinormcop(ox[, 1], ox[, 2], rho = Rho)
    contour(x, x, matrix(zedd, N, N), col = "blue", labcex = 1.5)

    ## End(Not run)

[Package VGAM version 1.0-3 Index]