Plackett {VGAM}R Documentation

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.

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.

Value

dplack gives the density, pplack gives the distribution function, and rplack 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

plackett, frank.

Examples

## Not run: 
N = 101
x = seq(0.0, 1.0, len=N)
oratio = exp(1)
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(r <- rplack(n=3000, oratio=oratio))
par(mfrow=c(1,2))
hist(r[,1]) # Should be uniform
hist(r[,2]) # Should be uniform
## End(Not run)

[Package VGAM version 0.7-7 Index]