# hinverse-methods: Methods for the Inverse of the h-functions In vines: Multivariate Dependence Modeling with Vines

## Description

The h^{-1} function represents the inverse of the h function with respect to its first argument. It should be defined for every copula used in a pair-copula construction (or it will be evaluated numerically).

## Usage

 `1` ```hinverse(copula, u, v, eps) ```

## Arguments

 `copula` A bivariate `copula` object. `u` Numeric vector with values in [0,1]. `v` Numeric vector with values in [0,1]. `eps` To avoid numerical problems for extreme values, the values of `u`, `v` and return values close to `0` and `1` are substituted by `eps` and `1 - eps`, respectively. The default `eps` value for most of the copulas is `.Machine\$double.eps^0.5`.

## Methods

`signature(copula = "copula")`

Default definition of the h^{-1} function for a bivariate copula. This method is used if no particular definition is given for a copula. The inverse is calculated numerically using the `uniroot` function.

`signature(copula = "indepCopula")`

The h^{-1} function of the Independence copula.

`signature(copula = "normalCopula")`

The h^{-1} function of the normal copula.

`signature(copula = "tCopula")`

The h^{-1} function of the t copula.

`signature(copula = "claytonCopula")`

The h^{-1} function of the Clayton copula.

`signature(copula = "frankCopula")`

The h^{-1} function of the Frank copula.

## References

Aas, K. and Czado, C. and Frigessi, A. and Bakken, H. (2009) Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44, 182–198.

Schirmacher, D. and Schirmacher, E. (2008) Multivariate dependence modeling using pair-copulas. Enterprise Risk Management Symposium, Chicago.

vines documentation built on May 2, 2019, 5:55 a.m.