khoudrajiCopula-class {copula} | R Documentation

## Class `"khoudrajiCopula"` and its Subclasses

### Description

The virtual class `"asymCopula"` of (conceptually) all asymmetric copulas and its ‘subclass’ `"asym2copula"` of those which are constructed from two copulas.

More specifically, the class `"khoudrajiCopula"` and its two subclasses `"khoudrajiBivCopula"` and `"khoudrajiExplicitCopula"` represent copulas constructed using Khoudraji's device from two copulas of the same dimension; see `khoudrajiCopula()` for more details.

### Objects from the Class

Objects are typically created via `khoudrajiCopula(...)`.

### Slots

As these classes extend `"copula"`, they have all its slots: `dimension`, `parameters`, `param.names`, `param.lowbnd`, `param.upbnd`, and `fullname`. The classes `"khoudrajiCopula"` and `"khoudrajiBivCopula"` have the extra slots

`copula1`:

  object of class `"copula"`.

`copula2`:

  second object of class `"copula"`.

In addition to these, the class `"khoudrajiExplicitCopula"` has the slots

`exprdist`:

  an `expression`, ...

`derExprs1`:

  an `expression` of length d, ...

`derExprs2`:

  an `expression` of length d, ...

### Methods

When possible, methods are defined at the `"khoudrajiCopula"` class level. The implementation of method `dCopula` for instance is however not possible at that level. In addition, it differs for `"khoudrajiBivCopula"` and `"khoudrajiExplicitCopula"` classes.

### References

Genest, C., Ghoudi, K., and Rivest, L.-P. (1998), Discussion of "Understanding relationships using copulas", by Frees, E., and Valdez, E., North American Actuarial Journal 3, 143–149.

Khoudraji, A. (1995), Contributions à l'étude des copules et àla modélisation des valeurs extrêmes bivariées, PhD thesis, Université Laval, Québec, Canada.

Liebscher, E. (2008), Construction of asymmetric multivariate copulas, Journal of Multivariate Analysis 99, 2234–2250.

### See Also

`khoudrajiCopula()`

### Examples

    showClass("khoudrajiCopula")# two subclasses

    ## all methods applicable to these subclasses:
    (meths <- sapply(names(getClass("khoudrajiCopula")@subclasses),
                     function(CL) methods(class = CL),
                     simplify=FALSE))

[Package copula version 0.999-15 Index]