Frank {VGAM}R Documentation

Frank's Bivariate Distribution

Description

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

Usage

dfrank(x1, x2, alpha)
pfrank(q1, q2, alpha)
rfrank(n, alpha)

Arguments

x1, x2, q1, q2 vector of quantiles.
n number of observations. Must be a positive integer of length 1.
alpha the positive association parameter alpha.

Details

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

Value

dfrank gives the density, pfrank gives the distribution function, and rfrank generates random deviates (a two-column matrix).

Author(s)

T. W. Yee

References

Genest, C. (1987) Frank's family of bivariate distributions. Biometrika, 74, 549–555.

See Also

frank.

Examples

## Not run: 
N = 100
x = seq(-0.30, 1.30, len=N)
alpha = 8
ox = expand.grid(x, x)
z = dfrank(ox[,1], ox[,2], alp=alpha)
contour(x, x, matrix(z, N, N))
z = pfrank(ox[,1], ox[,2], alp=alpha)
contour(x, x, matrix(z, N, N))

alpha = exp(4)
plot(r <- rfrank(n=3000, alpha=alpha))
par(mfrow=c(1,2))
hist(r[,1]) # Should be uniform
hist(r[,2]) # Should be uniform
## End(Not run)

[Package VGAM version 0.7-7 Index]