Frank {VGAM} | R Documentation

## Frank's Bivariate Distribution

### Description

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

### Usage

    dbifrankcop(x1, x2, apar, log = FALSE)
    pbifrankcop(q1, q2, apar)
    rbifrankcop(n, apar)

### Arguments

`x1, x2, q1, q2` | vector of quantiles.
`n` | number of observations. Same as in `runif`.
`apar` | the positive association parameter.
`log` | Logical. If `log = TRUE` then the logarithm of the density is returned.

### Details

See `bifrankcop`, the VGAM family functions for estimating the association parameter by maximum likelihood estimation, for the formula of the cumulative distribution function and other details.

### Value

`dbifrankcop` gives the density, `pbifrankcop` gives the distribution function, and `rbifrankcop` generates random deviates (a two-column matrix).

### Author(s)

T. W. Yee

### References

Genest, C. (1987) Frank's family of bivariate distributions. Biometrika, 74, 549–555.

### See Also

`bifrankcop`.

### Examples

    ## Not run: N <- 100; apar <- exp(2)
    xx <- seq(-0.30, 1.30, len = N)
    ox <- expand.grid(xx, xx)
    zedd <- dbifrankcop(ox[, 1], ox[, 2], apar = apar)
    contour(xx, xx, matrix(zedd, N, N))
    zedd <- pbifrankcop(ox[, 1], ox[, 2], apar = apar)
    contour(xx, xx, matrix(zedd, N, N))

    plot(rr <- rbifrankcop(n = 3000, apar = exp(4)))
    par(mfrow = c(1, 2))
    hist(rr[, 1]); hist(rr[, 2])  # Should be uniform

    ## End(Not run)

[Package VGAM version 1.1-1 Index]