Description Usage Arguments Details Value Author(s) References See Also Examples

Approximates the “density” of a copula by a piece-wise constant function.

1 2 |

`Cop` |
A function defining the copula. |

`dim` |
The approximation should be calculated on the dim-dimensional unit cube, defaults to 2. |

`depth` |
The number of hyperrectangles to be used to devide the unit cube, defaults to 10 for Approximation I and to 32 for Approximation II. |

`type` |
Whether Approximation I or Approximation II should be used, defaults to one. |

`TOL` |
A numerical tolerance used when calculating Approximation I. |

This function provides two methods for subdividing the *d*-dimensional unit cube into hyper-rectangles, with *d* being passed to the parameter `dim`

. As most of the functions in this package which create a new copula return a function that can be evaluated at points in arbitrary dimensions, it is necessary to specify for which dimension *d* one wishes to calculate the approximation to the copula's “density”.

The first method (Approximation I) determines *2^m* hyper-rectangles (where *m* is the parameter `depth`

), each containing the same probability mass with respect to the copula. The second method (Approximation II) dividies the unit cube into *m^d* hyper-squares.

These approximations can be interpreted as piecewise constant approximations of the copula's probability density function if the copula is absolutely continuous. For futher details see ‘References’.

`GetApprox`

returns an object of `class`

‘CopApprox’ according to its inputs. The returned object is a list containing a matrix that holds the information of the approximation, the argument `Cop`

, which approximation was determined, and other auxiliary information.

The only method for objects of class ‘CopApprox’ implemented so far are for the generic function `plot`

, and then only for the case if `dim`

was 2.

Berwin A. Turlach <berwin.turlach@gmail.com>

Tajvidi, N. and Turlach, B.A. (2017). A general approach to generate random variates for multivariate copulae, *Australian & New Zealand Journal of Statistics*. Doi:10.1111/anzs.12209.

1 2 3 | ```
Cop <- NewMEVGumbelCopula(3)
CopApprox <- GetApprox(Cop, dim=2)
plot(CopApprox)
``` |

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