R: Plackett's Bivariate Copula

Biplackett {VGAM} | R Documentation

## 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)

### 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.

### 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.

### Value

`dbiplackcop` gives the density, `pbiplackcop` gives the distribution function, and `rbiplackcop` 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

`biplackettcop`, `bifrankcop`.

### Examples

    ## Not run:  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

    ## End(Not run)

[Package VGAM version 1.1-3 Index]