# bifrankcopUC: Frank's Bivariate Distribution In VGAM: Vector Generalized Linear and Additive Models

 Frank 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).

T. W. Yee

### References

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

`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)
``````

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.