VGAM (version 0.8-3)

Plackett: Plackett's Bivariate Distribution

Description

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

Usage

dplack(x1, x2, oratio, log=FALSE)
pplack(q1, q2, oratio)
rplack(n, oratio)

Arguments

x1, x2, q1, q2

vector of quantiles.

n

number of observations. Must be a positive integer of length 1.

oratio

the positive odds ratio $\psi$.

log

Logical. If TRUE then the logarithm is returned.

Value

• dplack gives the density, pplack gives the distribution function, and rplack generates random deviates (a two-column matrix).

Details

See plackett, 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

plackett, frank.

Examples

N = 101; oratio = exp(1)
x = seq(0.0, 1.0, len=N)
ox = expand.grid(x, x)
z = dplack(ox[,1], ox[,2], oratio=oratio)
contour(x, x, matrix(z, N, N), col="blue")
z = pplack(ox[,1], ox[,2], oratio=oratio)
contour(x, x, matrix(z, N, N), col="blue")

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