VGAM (version 1.1-12)

Frank: Frank's Bivariate Distribution

Description

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

Usage

dbifrankcop(x1, x2, apar, log = FALSE)
pbifrankcop(q1, q2, apar)
rbifrankcop(n, apar)

Value

dbifrankcop gives the density,

pbifrankcop gives the distribution function, and

rbifrankcop generates random deviates (a two-column matrix).

Arguments

x1, x2, q1, q2

vector of quantiles.

n

number of observations. Same as in runif.

apar

the positive association parameter.

log

Logical. If log = TRUE then the logarithm of the density is returned.

Author

T. W. Yee

Details

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

References

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

See Also

bifrankcop.

Examples

if (FALSE) N <- 100; apar <- exp(2)
xx <- seq(-0.30, 1.30, len = N)
ox <- expand.grid(xx, xx)
zedd <- dbifrankcop(ox[, 1], ox[, 2], apar = apar)
contour(xx, xx, matrix(zedd, N, N))
zedd <- pbifrankcop(ox[, 1], ox[, 2], apar = apar)
contour(xx, xx, matrix(zedd, N, N))

plot(rr <- rbifrankcop(n = 3000, apar = exp(4)))
par(mfrow = c(1, 2))
hist(rr[, 1]); hist(rr[, 2])  # Should be uniform