biplackettcopUC: Plackett's Bivariate Copula

In VGAM: Vector Generalized Linear and Additive Models

Plackett's Bivariate Copula

Description

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

Usage

dbiplackcop(x1, x2, oratio, log = FALSE)
pbiplackcop(q1, q2, oratio)
rbiplackcop(n, oratio)

Arguments

x1, x2, q1, q2	vector of quantiles.
n	number of observations. Same as in runif.
oratio	the positive odds ratio \psi.
log	Logical. If TRUE then the logarithm is returned.

Details

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

Value

dbiplackcop gives the density, pbiplackcop gives the distribution function, and rbiplackcop generates random deviates (a two-column matrix).

Author(s)

T. W. Yee

References

Mardia, K. V. (1967). Some contributions to contingency-type distributions. Biometrika, 54, 235–249.

See Also

biplackettcop, bifrankcop.

Examples

## Not run:  N <- 101; oratio <- exp(1)
x <- seq(0.0, 1.0, len = N)
ox <- expand.grid(x, x)
zedd <- dbiplackcop(ox[, 1], ox[, 2], oratio = oratio)
contour(x, x, matrix(zedd, N, N), col = "blue")
zedd <- pbiplackcop(ox[, 1], ox[, 2], oratio = oratio)
contour(x, x, matrix(zedd, N, N), col = "blue")

plot(rr <- rbiplackcop(n = 3000, oratio = oratio))
par(mfrow = c(1, 2))
hist(rr[, 1])  # Should be uniform
hist(rr[, 2])  # Should be uniform

## End(Not run)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.