gevr

Likelihood, score function and information matrix,
approximate ancillary statistics and sample space derivative
for the generalized extreme value distribution parametrized in terms of the return level \(z\), scale and shape.

Various tools for the analysis of univariate, multivariate and functional extremes. Exact simulation from max-stable processes [Dombry, Engelke and Oesting (2016) <doi:10.1093/biomet/asw008>, R-Pareto processes for various parametric models, including Brown-Resnick (Wadsworth and Tawn, 2014, <doi:10.1093/biomet/ast042>) and Extremal Student (Thibaud and Opitz, 2015, <doi:10.1093/biomet/asv045>). Threshold selection methods, including Wadsworth (2016) <doi:10.1080/00401706.2014.998345>, and Northrop and Coleman (2014) <doi:10.1007/s10687-014-0183-z>. Multivariate extreme diagnostics. Estimation and likelihoods for univariate extremes, e.g., Coles (2001) <doi:10.1007/978-1-4471-3675-0>.

Leo Belzile

Modelling of Extreme Values

Jennifer L. Wadsworth

Paul J. Northrop

Scott D. Grimshaw

Jin Zhang

Michael A. Stephens

Art B. Owen

Raphael Huser

gevr function

<dl><dt>par</dt>
<dd>vector of <code>retlev</code>, <code>scale</code> and <code>shape</code></dd>
<dt>dat</dt>
<dd>sample vector</dd>
<dt>p</dt>
<dd>tail probability, corresponding to \((1-p)\)th quantile for \(z\)</dd>
<dt>method</dt>
<dd>string indicating whether to use the expected (<code>'exp'</code>) or the observed (<code>'obs'</code> - the default) information matrix.</dd>
<dt>nobs</dt>
<dd>number of observations</dd>
<dt>V</dt>
<dd>vector calculated by <code>gevr.Vfun</code></dd></dl>

Arguments

<pre><code>gevr.ll(par, dat, p)
gevr.ll.optim(par, dat, p)
gevr.score(par, dat, p)
gevr.infomat(par, dat, p, method = c('obs', 'exp'), nobs = length(dat))
gevr.Vfun(par, dat, p)
gevr.phi(par, dat, p, V)
gevr.dphi(par, dat, p, V)</code></pre>

Usage

<ul>
<li><code>gevr.ll</code>: log likelihood</li>
<li><code>gevr.ll.optim</code>: negative log likelihood parametrized in terms of return levels, <code>log(scale)</code> and shape in order to perform unconstrained optimization</li>
<li><code>gevr.score</code>: score vector</li>
<li><code>gevr.infomat</code>: observed information matrix</li>
<li><code>gevr.Vfun</code>: vector implementing conditioning on approximate ancillary statistics for the TEM</li>
<li><code>gevr.phi</code>: canonical parameter in the local exponential family approximation</li>
<li><code>gevr.dphi</code>: derivative matrix of the canonical parameter in the local exponential family approximation</li>
</ul>

Functions

Author

Generalized extreme value distribution (return level parametrization) — gevr

<dl>

<dt>par</dt>
<dd>vector of <code>retlev</code>, <code>scale</code> and <code>shape</code></dd>


<dt>dat</dt>
<dd>sample vector</dd>


<dt>p</dt>
<dd>tail probability, corresponding to \((1-p)\)th quantile for \(z\)</dd>


<dt>method</dt>
<dd>string indicating whether to use the expected (<code>'exp'</code>) or the observed (<code>'obs'</code> - the default) information matrix.</dd>


<dt>nobs</dt>
<dd>number of observations</dd>


<dt>V</dt>
<dd>vector calculated by <code>gevr.Vfun</code></dd>

</dl>

<ul>
<li><code>gevr.ll</code>: log likelihood</li>
<li><code>gevr.ll.optim</code>: negative log likelihood parametrized in terms of return levels, <code>log(scale)</code> and shape in order to perform unconstrained optimization</li>
<li><code>gevr.score</code>: score vector</li>
<li><code>gevr.infomat</code>: observed information matrix</li>
<li><code>gevr.Vfun</code>: vector implementing conditioning on approximate ancillary statistics for the TEM</li>
<li><code>gevr.phi</code>: canonical parameter in the local exponential family approximation</li>
<li><code>gevr.dphi</code>: derivative matrix of the canonical parameter in the local exponential family approximation</li>
</ul>

gevr: Generalized extreme value distribution (return level parametrization)

Description

Arguments

Usage

Functions

Author