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)
x1, x2, q1, q2 |
vector of quantiles. |
n |
number of observations.
Same as in |
apar |
the positive association parameter. |
log |
Logical.
If |
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.
dbifrankcop gives the density,
pbifrankcop gives the distribution function, and
rbifrankcop generates random deviates (a two-column matrix).
T. W. Yee
Genest, C. (1987). Frank's family of bivariate distributions. Biometrika, 74, 549–555.
## Not run: 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 ## End(Not run)
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