PiecewisePareto_CDF

Calculates the cumulative distribution function of a Piecewise Pareto Distribution. This function is deprecated. Use <code>pPiecewisePareto</code> instead.

Utilities for the Pareto, piecewise Pareto and generalized Pareto distribution
that are useful for reinsurance pricing. In particular, the package provides
a non-trivial algorithm that can be used to match the expected losses of a
tower of reinsurance layers with a layer-independent collective risk model.
The theoretical background of the matching algorithm and most other methods
are described in Ulrich Riegel (2018) <doi:10.1007/s13385-018-0177-3>.

Ulrich Riegel

Pareto

The Pareto, Piecewise Pareto and Generalized Pareto Distribution

PiecewisePareto_CDF function

<dl><dt>x</dt>
<dd>Numeric. The function evaluates the CDF at <code>x</code>.</dd>
<dt>t</dt>
<dd>Numeric vector. Thresholds of the piecewise Pareto distribution.</dd>
<dt>alpha</dt>
<dd>Numeric vector. <code>alpha[i]</code> is the Pareto alpha in excess of <code>t[i]</code>.</dd>
<dt>truncation</dt>
<dd>Numeric. If <code>truncation</code> is not <code>NULL</code> and <code>truncation &gt; t</code>, then the distribution is truncated at <code>truncation</code>.</dd>
<dt>truncation_type</dt>
<dd>Character. If <code>truncation_type = "wd"</code> then the whole distribution is truncated. If <code>truncation_type = "lp"</code> then a truncated Pareto is used for the last piece.</dd></dl>

Arguments

Distribution Function of the Piecewise Pareto Distribution — PiecewisePareto_CDF

<dl>

<dt>x</dt>
<dd>Numeric. The function evaluates the CDF at <code>x</code>.</dd>


<dt>t</dt>
<dd>Numeric vector. Thresholds of the piecewise Pareto distribution.</dd>


<dt>alpha</dt>
<dd>Numeric vector. <code>alpha[i]</code> is the Pareto alpha in excess of <code>t[i]</code>.</dd>


<dt>truncation</dt>
<dd>Numeric. If <code>truncation</code> is not <code>NULL</code> and <code>truncation &gt; t</code>, then the distribution is truncated at <code>truncation</code>.</dd>


<dt>truncation_type</dt>
<dd>Character. If <code>truncation_type = "wd"</code> then the whole distribution is truncated. If <code>truncation_type = "lp"</code> then a truncated Pareto is used for the last piece.</dd>

</dl>

PiecewisePareto_CDF: Distribution Function of the Piecewise Pareto Distribution

Description

Usage

Value

Arguments

References

Examples