phi.inv

The Archimedean generator function and its inverse.

phi, phi.inv

Package provides the estimation of the structure and the parameters, sampling methods and structural plots of Hierarchical Archimedean Copulae (HAC).

Gong Chen

Estimation, Simulation and Visualization of Hierarchical
Archimedean Copulae (HAC)

Ostap Okhrin

Alexander Ristig

phi, phi.inv function

<dl> <dt>x</dt>
<dd>a scalar, vector or matrix at which the function is evaluated. The support of the functions has to be taken into account, i.e. \(x \in [0, \infty]\) for the generator function and \(x \in [0, 1]\) for its inverse.</dd> <dt>theta</dt>
<dd>the feasible copula parameter, i.e. \(\theta \in [1, \infty)\) for the Gumbel and Joe family, \(\theta \in (0, \infty)\) for the Clayton and Frank family and \(\theta \in [0, 1)\) for the Ali-Mikhail-Haq family.</dd><dt>type</dt>
<dd>select between the following integer numbers for specifying the <code>type</code> of the hierarchical Archimedean copula (HAC) or Archimedean copula (AC):<ul>
<li><code> 1</code> = HAC Gumbel</li>
<li><code> 2</code> = AC Gumbel</li>
<li><code> 3</code> = HAC Clayton</li>
<li><code> 4</code> = AC Clayton</li>
<li><code> 5</code> = HAC Frank</li>
<li><code> 6</code> = AC Frank</li>
<li><code> 7</code> = HAC Joe</li>
<li><code> 8</code> = AC Joe</li>
<li><code> 9</code> = HAC Ali-Mikhail-Haq</li>
<li><code>10</code> = AC Ali-Mikhail-Haq</li>
</ul></dd></dl>

Arguments

Generator function — phi, phi.inv

<dl>

 <dt>x</dt>
<dd>a scalar, vector or matrix at which the function is evaluated. The support of the functions has to be taken into account, i.e. \(x \in [0, \infty]\) for the generator function and \(x \in [0, 1]\) for its inverse.</dd>

 <dt>theta</dt>
<dd>the feasible copula parameter, i.e. \(\theta \in [1, \infty)\) for the Gumbel and Joe family, \(\theta \in (0, \infty)\) for the Clayton and Frank family and \(\theta \in [0, 1)\) for the Ali-Mikhail-Haq family.</dd>

<dt>type</dt>
<dd>select between the following integer numbers for specifying the <code>type</code> of the hierarchical Archimedean copula (HAC) or Archimedean copula (AC):<ul>
<li><code> 1</code> = HAC Gumbel</li>
<li><code> 2</code> = AC Gumbel</li>
<li><code> 3</code> = HAC Clayton</li>
<li><code> 4</code> = AC Clayton</li>
<li><code> 5</code> = HAC Frank</li>
<li><code> 6</code> = AC Frank</li>
<li><code> 7</code> = HAC Joe</li>
<li><code> 8</code> = AC Joe</li>
<li><code> 9</code> = HAC Ali-Mikhail-Haq</li>
<li><code>10</code> = AC Ali-Mikhail-Haq</li>
</ul></dd>

</dl>

phi, phi.inv: Generator function

Description

Usage

Arguments

Examples