Frank {VGAM} | R Documentation

## Frank's Bivariate Distribution

### Description

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

### Usage

    dfrank(x1, x2, alpha, log=FALSE)
    pfrank(q1, q2, alpha)
    rfrank(n, alpha)

### Arguments

`x1, x2, q1, q2` | vector of quantiles.
`n` | number of observations. Must be a positive integer of length 1.
`alpha` | the positive association parameter alpha.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### Details

See `frank`, 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

`dfrank` gives the density, `pfrank` gives the distribution function, and `rfrank` 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

`frank`.

### Examples

    ## Not run:
    N = 100
    x = seq(-0.30, 1.30, len=N)
    alpha = 8
    ox = expand.grid(x, x)
    z = dfrank(ox[,1], ox[,2], alp=alpha)
    contour(x, x, matrix(z, N, N))
    z = pfrank(ox[,1], ox[,2], alp=alpha)
    contour(x, x, matrix(z, N, N))

    alpha = exp(4)
    plot(r <- rfrank(n=3000, alpha=alpha))
    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]