VGAM (version 0.9-0)

Fgm: Farlie-Gumbel-Morgenstern's Bivariate Distribution

Description

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

Usage

dfgm(x1, x2, alpha, log = FALSE)
pfgm(q1, q2, alpha)
rfgm(n, alpha)

Arguments

x1, x2, q1, q2

vector of quantiles.

n

number of observations. Must be a positive integer of length 1.

alpha

the association parameter.

log

Logical. If TRUE then the logarithm is returned.

Value

• dfgm gives the density, pfgm gives the distribution function, and rfgm generates random deviates (a two-column matrix).

Details

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

See Also

fgm.

Examples

N = 101; x = seq(0.0, 1.0, len = N); alpha = 0.7
ox = expand.grid(x, x)
z = dfgm(ox[,1], ox[,2], alpha=alpha)
contour(x, x, matrix(z, N, N), col="blue")
z = pfgm(ox[,1], ox[,2], alpha=alpha)
contour(x, x, matrix(z, N, N), col="blue")

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