VGAM (version 1.0-4)

# Binormcop: 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.

## Value

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

## 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.

`binormalcop`, `binormal`.

## Examples

Run this code
``````# 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)
# }
``````

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