Frank's Bivariate Distribution

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

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

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.

Value

dbifrankcop gives the density, pbifrankcop gives the distribution function, and rbifrankcop generates random deviates (a two-column matrix).

References

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

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.

See also

bifrankcop.

Examples

if (FALSE) N <- 100; apar <- exp(2)
xx <- seq(-0.30, 1.30, len = N)
#> Error: object 'N' not found
ox <- expand.grid(xx, xx)
#> Error: object 'xx' not found
zedd <- dbifrankcop(ox[, 1], ox[, 2], apar = apar)
#> Error: object 'ox' not found
contour(xx, xx, matrix(zedd, N, N))
#> Error: object 'xx' not found
zedd <- pbifrankcop(ox[, 1], ox[, 2], apar = apar)
#> Error: object 'ox' not found
contour(xx, xx, matrix(zedd, N, N))
#> Error: object 'xx' not found

plot(rr <- rbifrankcop(n = 3000, apar = exp(4)))

par(mfrow = c(1, 2))
hist(rr[, 1]); hist(rr[, 2])  # Should be uniform

 # \dontrun{}