# bifgmcopUC: Farlie-Gumbel-Morgenstern's Bivariate Distribution In VGAM: Vector Generalized Linear and Additive Models

 Bifgmcop R Documentation

## Farlie-Gumbel-Morgenstern's Bivariate Distribution

### Description

Density, distribution function, and random generation for the (one parameter) bivariate Farlie-Gumbel-Morgenstern's distribution.

### Usage

``````dbifgmcop(x1, x2, apar, log = FALSE)
pbifgmcop(q1, q2, apar)
rbifgmcop(n, apar)
``````

### Arguments

 `x1, x2, q1, q2` vector of quantiles. `n` number of observations. Same as in `runif`. `apar` the association parameter. `log` Logical. If `TRUE` then the logarithm is returned.

### Details

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

### Value

`dbifgmcop` gives the density, `pbifgmcop` gives the distribution function, and `rbifgmcop` generates random deviates (a two-column matrix).

### Author(s)

T. W. Yee

`bifgmcop`.

### Examples

``````## Not run:  N <- 101; x <- seq(0.0, 1.0, len = N); apar <- 0.7
ox <- expand.grid(x, x)
zedd <- dbifgmcop(ox[, 1], ox[, 2], apar = apar)
contour(x, x, matrix(zedd, N, N), col = "blue")
zedd <- pbifgmcop(ox[, 1], ox[, 2], apar = apar)
contour(x, x, matrix(zedd, N, N), col = "blue")

plot(r <- rbifgmcop(n = 3000, apar = apar), col = "blue")
par(mfrow = c(1, 2))
hist(r[, 1])  # Should be uniform
hist(r[, 2])  # Should be uniform

## End(Not run)
``````

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.