VGAM (version 0.9-3)

Biclaytoncop: Clayton Copula (Bivariate) Distribution

Description

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

Usage

dbiclaytoncop(x1, x2, alpha = 0, log = FALSE)
rbiclaytoncop(n, alpha = 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.

alpha

the association parameter. Should be in the interval $[0, \infty)$. The default corresponds to independence.

log

Logical. If TRUE then the logarithm is returned.

Value

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

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.

References

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

See Also

binormalcop, binormal.

Examples

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], alpha = 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)