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 0.7-9 Index]