VGAM (version 1.1-12)

Biplackett: 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)

Value

dbiplackcop gives the density,

pbiplackcop gives the distribution function, and

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

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.

Author

T. W. Yee

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.

References

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

See Also

biplackettcop, bifrankcop.

Examples

if (FALSE)  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