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

 Biclaytoncop R Documentation

## Clayton Copula (Bivariate) Distribution

### Description

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

### Usage

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, \infty). 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.

### Examples

## 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)

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