# biclaytoncopUC: Clayton Copula (Bivariate) Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Density and random generation for the (one parameter) bivariate Clayton copula distribution.

## Usage

 ```1 2``` ```dbiclaytoncop(x1, x2, apar = 0, log = FALSE) rbiclaytoncop(n, apar = 0) ```

## Arguments

 `x1, x2` vector of quantiles. The `x1` and `x2` should both be in the interval (0,1). `n` number of observations. Same as `rnorm`. `apar` the association parameter. Should be in the interval [0, Inf). The default corresponds to independence. `log` Logical. If `TRUE` then the logarithm is returned.

## Details

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

## Value

`dbiclaytoncop` gives the density at point (`x1`,`x2`), `rbiclaytoncop` generates random deviates (a two-column matrix).

## Note

`dbiclaytoncop()` does not yet handle `x1 = 0` and/or `x2 = 0`.

## Author(s)

R. Feyter and T. W. Yee

## References

Clayton, D. (1982). A model for association in bivariate survival data. Journal of the Royal Statistical Society, Series B, Methodological, 44, 414–422.

`biclaytoncop`, `binormalcop`, `binormal`.
 ```1 2 3 4 5 6 7 8``` ```## Not run: edge <- 0.01 # A small positive value N <- 101; x <- seq(edge, 1.0 - edge, len = N); Rho <- 0.7 ox <- expand.grid(x, x) zedd <- dbiclaytoncop(ox[, 1], ox[, 2], apar = Rho, log = TRUE) par(mfrow = c(1, 2)) contour(x, x, matrix(zedd, N, N), col = "blue", labcex = 1.5, las = 1) plot(rbiclaytoncop(1000, 2), col = "blue", las = 1) ## End(Not run) ```