# binormcopUC: Gaussian Copula (Bivariate) Distribution

### Description

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

### Usage

 ```1 2 3``` ```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

`binormalcop`, `binormal`.

### Examples

 ```1 2 3 4 5 6 7 8 9``` ```## 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) ```

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