AoE-package {AoE}R Documentation

Analysis of Extremes

Description

The package provides functions for some selected procedures in univariate and multivariate extreme value analysis. It has grown over a number of years as a complement to executive courses for the Dutch and Belgian Actuarial Associations. Its aim is mainly pedagogical, and no aim whatsoever is made to provide a comprehensive toolset for extreme value analysis.

Details

Package: AoE
Type: Package
Version: 1.0.1
Date: 2008-04-11
License: Gnu General Public License version 2

The functions can be divided into a number of different categories; see below. Moreover, the package provides some data-sets as well.

Diagnostic plots
Hill.diagnostic
MEplot

Estimators of tail parameters
GPD_par
Hill
ML
Moment

Parametric distribution fitting
fitGPD
fitPareto

Estimators of tail-related risk measures
Burr.empirical
Burr.Weissman
EconomicCapital
ExcessLoss
Expectation
ExpectedShortfall
PHtransform
RiskMeasure
TailQuantile
Variance
Weissman.q

Threshold selection
ChooseK
TQ_ChooseK

Bivariate tail dependence
AngularMeasure
ETDF
PickandsDF
TailProb_sum
TailQuantile_sum

Temporal dependence of extremes
ExtremalIndex

Data-sets
ABN, ING
Loss, ALAE
norwegian
soa
top40

Random number generation
rbivcauchy
rbivnorm
rburr
UvT_Cat

Author(s)

Johan Segers johan.segers@uclouvain.be, gratefully acknowledging valuable input and patient bug checking from John H.J. Einmahl (Tilburg University) as well as stimulating comments from course participants of the Actuarieel Instituut (the Netherlands) and the ARAB-KVBA (Belgium).

References

Beirlant, J., Goegebeur, Y., Segers, J., and Teugels, J. (2004). Statistics of Extremes. Wiley, Chichester. http://lstat.kuleuven.be/Wiley/index.html

Embrechts, P., Klueppelberg, C., and Mikosch, T. (1997). Modelling Extremal Events For Insurance And Finance. Springer.

de Haan, L. and Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer.

Examples

# Hill estimator
x <- 1/runif(100)
Hill(1/runif(100), CI.p = 0.95)
abline(h = 1, col = "blue")

# tail quantile and excess-of-loss net premium
data(Loss)
TailQuantile(Loss, p = 0.001, k = 25:200)
ExcessLoss(Loss, a = 1.2e6, k = 25:200)

# empirical tail dependence function
data(Loss, ALAE)
ETDF(data.x = Loss, data.y = ALAE, k = 10:100)

# angular measure
AngularMeasure(data = rbivcauchy(1000), k = c(20, 50), method = "c")
abline(a = 0, b = 1, col = "red")

# extremal index
data(ABN)
ExtremalIndex(-ABN[2000:2500], threshold = 0.05, plot = TRUE)

[Package AoE version 1.0.1 Index]