fitdGPD

Given a sample of exceedances, estimate the parameters via maximum likelihood along with \(1-\alpha\) level confidence intervals.

A set of procedures for estimating risks related to extreme events via risk measures such as Expectile, Value-at-Risk, etc. is provided. Estimation methods for univariate independent observations and temporal dependent observations are available. The methodology is extended to the case of independent multidimensional observations. The statistical inference is performed through parametric and non-parametric estimators. Inferential procedures such as confidence intervals, confidence regions and hypothesis testing are obtained by exploiting the asymptotic theory. Adapts the methodologies derived in Padoan and Stupfler (2022) <doi:10.3150/21-BEJ1375>, Davison et al. (2023) <doi:10.1080/07350015.2022.2078332>, Daouia et al. (2018) <doi:10.1111/rssb.12254>, Drees (2000) <doi:10.1214/aoap/1019487617>, Drees (2003) <doi:10.3150/bj/1066223272>, de Haan and Ferreira (2006) <doi:10.1007/0-387-34471-3>, de Haan et al. (2016) <doi:10.1007/s00780-015-0287-6>, Padoan and Rizzelli (2024) <doi:10.3150/23-BEJ1668>, Daouia et al. (2024) <doi:10.3150/23-BEJ1632>.

Simone Padoan

ExtremeRisks

Extreme Risk Measures

Gilles Stupfler

Carlotta Pacifici

fitdGPD function

<dl><dt>excess</dt>
<dd>vector of positive exceedances, i.e., \(Y - t \mid Y &gt; t\), with \(t\) being the threshold</dd>
<dt>alpha</dt>
<dd>level for confidence interval of scale and shape parameters. Default: 0.05, giving 95% confidence intervals</dd></dl>

Arguments

Maximum likelihood estimation of the parameters of the discrete generalized Pareto distribution — fitdGPD

<dl>

<dt>excess</dt>
<dd>vector of positive exceedances, i.e., \(Y - t \mid Y &gt; t\), with \(t\) being the threshold</dd>


<dt>alpha</dt>
<dd>level for confidence interval of scale and shape parameters. Default: 0.05, giving 95% confidence intervals</dd>

</dl>

fitdGPD: Maximum likelihood estimation of the parameters of the discrete generalized Pareto distribution

Description

Usage

Value

Arguments

References

Examples