Plackett's Bivariate Copula

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.

Value

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

References

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

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.

Examples

if (FALSE)  N <- 101; oratio <- exp(1)
x <- seq(0.0, 1.0, len = N)
#> Error: object 'N' not found
ox <- expand.grid(x, x)
#> Error: object 'x' not found
zedd <- dbiplackcop(ox[, 1], ox[, 2], oratio = oratio)
#> Error: object 'ox' not found
contour(x, x, matrix(zedd, N, N), col = "blue")
#> Error: object 'x' not found
zedd <- pbiplackcop(ox[, 1], ox[, 2], oratio = oratio)
#> Error: object 'ox' not found
contour(x, x, matrix(zedd, N, N), col = "blue")
#> Error: object 'x' not found

plot(rr <- rbiplackcop(n = 3000, oratio = oratio))

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

 # \dontrun{}