R: Clayton Copula (Bivariate) Distribution

Biclaytoncop {VGAM} | 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, 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.

### See Also

`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)

[Package VGAM version 1.0-3 Index]