Likelihood, score function and information matrix for the Poisson process likelihood.

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

pp function

<dl><dt>par</dt>
<dd>vector of <code>loc</code>, <code>scale</code> and <code>shape</code></dd>
<dt>dat</dt>
<dd>sample vector</dd>
<dt>u</dt>
<dd>threshold</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>np</dt>
<dd>number of periods of observations. This is a post hoc adjustment for the intensity so that the parameters of the model coincide with those of a generalized extreme value distribution with block size <code>length(dat)/np</code>.</dd>
<dt>nobs</dt>
<dd>number of observations for the expected information matrix. Default to <code>length(dat)</code> if <code>dat</code> is provided.</dd></dl>

Arguments

<pre><code>pp.ll(par, dat)
pp.ll(par, dat, u, np)
pp.score(par, dat)
pp.infomat(par, dat, method = c('obs', 'exp'))</code></pre>

Usage

<ul>
<li><code>pp.ll</code>: log likelihood</li>
<li><code>pp.score</code>: score vector</li>
<li><code>pp.infomat</code>: observed or expected information matrix</li>
</ul>

Functions

Author

Poisson process of extremes. — pp

<dl>

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


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


<dt>u</dt>
<dd>threshold</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>np</dt>
<dd>number of periods of observations. This is a post hoc adjustment for the intensity so that the parameters of the model coincide with those of a generalized extreme value distribution with block size <code>length(dat)/np</code>.</dd>


<dt>nobs</dt>
<dd>number of observations for the expected information matrix. Default to <code>length(dat)</code> if <code>dat</code> is provided.</dd>

</dl>

<pre><code>pp.ll(par, dat)
pp.ll(par, dat, u, np)
pp.score(par, dat)
pp.infomat(par, dat, method = c('obs', 'exp'))</code></pre>

<ul>
<li><code>pp.ll</code>: log likelihood</li>
<li><code>pp.score</code>: score vector</li>
<li><code>pp.infomat</code>: observed or expected information matrix</li>
</ul>

pp: Poisson process of extremes.

Description

Arguments

Usage

Functions

Author

References