Renext-package {Renext}

Renewal Method for Extreme Values Extrapolation

Description

This package proposes fits and diagnostics for the so-called méthode du renouvellement, an alternative to other "Peaks Over Threshold" (POT) methods. The méthode du renouvellement generalises the classical POT by allowing the excesses over the threshold to follow a probability distribution which can differ from the Generalised Pareto Distribution (GPD). Weibull or gamma excesses are sometimes preferred to GPD excesses. The special case of exponential excesses (which falls in the three families: GPD, Weibull and gamma) has a special interest since it allows exact inference for the (scalar) parameter and for the quantiles form OT data (only).

The package allows the joint use of possibly three kinds of data or information. The first kind is classical excesses, or "OT data". It can be completed with two kinds of data resulting from a temporal aggregation, as is often the case for historical data. Both types are optional, and concern periods or blocks that must not overlap nor cross the OT period.

• MAX data correspond to the case where one knows the r largest observations over each block. The number r may vary across blocks. This kind of data is often called 'r largest', or "r Largest Order Statistics" (r LOS).

• OTS data (for OT Supplementary data) correspond to the case where one knows for each block b all the observations that exceeded a threshold u_b which is greater (usually much greater) than the main threshold u. The number r_b of such observations can be zero, in which case we may say that u_b is an unobserved level. A threshold u_b is sometimes called a perception threshold.

Historical data are often available in hydrology (e.g. for river flood discharges, for sea-levels or sea surges) and can concern large periods such as past centuries. An unobserved level can typically be related to a material benchmark.

Maximum likelihood estimation is made possible in this context of heterogeneous data. Inference is based on the asymptotic normality of parameter vector estimate and on linearisation ("delta method") for quantiles or parameter functions.

The package allows the use of "marked-process observations" data (datetime of event and level) where an interevent analysis can be useful. It also allows the event dates to be unknown and replaced by a much broader block indication, e.g. a year number. The key point is then that the "effective duration" (total duration of observation periods) is known. Event counts for blocks can be used to check the assumption of Poisson-distributed events.

The package development was initiated, directed and financed by the french Institut de Radioprotection et de Sûreté Nucléaire (IRSN). The package is a non-academic tool designed for applied analysis on case studies and investigations or comparisons on classical probabilistic models.

Details

The DESCRIPTION file:

Package:	Renext
Type:	Package
Title:	Renewal Method for Extreme Values Extrapolation
Version:	3.1-4
Date:	2023-08-29
Author:	Yves Deville <[e-mail]>, Lise Bardet <[e-mail]>
Maintainer:	Yann Richet <[e-mail]>
URL:	https://github.com/IRSN/Renext
Depends:	R (>= 2.8.0), stats, graphics, evd
Imports:	numDeriv, splines, methods
Suggests:	MASS, ismev, XML
Description:	Peaks Over Threshold (POT) or 'methode du renouvellement'. The distribution for the excesses can be chosen, and heterogeneous data (including historical data or block data) can be used in a Maximum-Likelihood framework.
License:	GPL (>= 2)
LazyData:	yes

Index of help topics:

Brest                   Surge heights at Brest
Brest.years             Surge heights at Brest partial data
Brest.years.missing     Years with missing periods in 'Brest.year'
                        dataset
CV2                     Squared Coefficient of Variation
CV2.test                CV2 test of exponentiality
Dunkerque               Surge heights at Dunkerque
EM.mixexp               Expectation-Maximisation for a mixture of
                        exponential distributions
GPD                     Generalised Pareto Distribution
Garonne                 Flow of the french river La Garonne
Hpoints                 Plotting positions for exponential return
                        levels
Jackson                 Jackson's statistic
Jackson.test            Jackson's test of exponentiality
LRExp                   Likelihood Ratio statistic for exponential vs.
                        GPD
LRExp.test              Likelihood Ratio test of exponentiality vs. GPD
LRGumbel                Likelihood Ratio statistic for Gumbel vs. GEV
LRGumbel.test           Likelihood Ratio test for the Gumbel
                        distribution
Lomax                   Lomax distribution
Maxlo                   'maxlo' distribution
MixExp2                 Mixture of two exponential distributions
NBlevy                  Negative Binomial Levy process
OT2MAX                  Temporal aggregation of a Marked Process
OTjitter                Add a small amount of noise to a numeric vector
PPplot                  Diagnostic plots for Renouv objects
RLlegend                Legend management for return level plots
RLpar                   Graphical parameters for Return Level plots
RLplot                  Return level plot
Ren2gev                 Translate a vector of coefficients from a
                        Renewal-POT model with Pareto excesses into a
                        vector of GEV parameters
Ren2gumbel              Translate a vector of coefficients from a
                        Renewal-POT model with exponential excesses to
                        a vector of Gumbel parameters
Renext-package          Renewal Method for Extreme Values Extrapolation
Renouv                  Fit a 'Renouvellement' model
RenouvNoEst             Define a 'renouvellement' model without
                        estimation
SLTW                    Shifted Left Truncated Weibull (SLTW)
                        distribution
SandT                   Compute empirical survivals (S) and return
                        periods (T)
anova.Renouv            Compute an analysis of deviance table for two
                        nested Renouv objects
barplotRenouv           Barplot for Renouv "Over Threshold" counts
expplot                 Classical "exponential distribution" plot
fGEV.MAX                Fit a GEV distribution from block maxima or r
                        largest order statistics using an aggregated
                        Renewal POT process
fGPD                    Fit a two-parameters Generalised Pareto
                        Distribution from a sample
fgamma                  ML estimation of the Gamma distribution
flomax                  ML estimation of the Lomax distribution
fmaxlo                  ML estimation of a 'maxlo' distribution
fweibull                ML estimation of classical Weibull distribution
gev2Ren                 Translate a vector of GEV parameters into
                        renewal model
gof.date                Goodness-of-fit for the distribution of dates
gofExp.test             Goodness-of-fit test for exponential
                        distribution
gumbel2Ren              Translate a vector of Gumbel parameters into a
                        vector of parameters for a renewal model
ini.mixexp2             Simple estimation for the mixture of two
                        exponential distributions
interevt                Interevents (or interarrivals) from events
                        dates
logLik.Renouv           Log-likelihood of a "Renouv" object
mom.mixexp2             Moment estimation for the mixture of two
                        exponential distributions
mom2par                 Parameters from moments
pGreenwood1             Probability that the Greenwood's statistic is
                        smaller than one
parDeriv                Derivation of probability functions with
                        respect to the parameters
parIni.MAX              Initial estimation of GPD parameters for an
                        aggregated renewal model
plot.Rendata            Plot a Rendata object
plot.Renouv             Plot an object of class "Renouv"
predict.Renouv          Compute return levels and confidence limits for
                        a "Renouv" object
qStat                   Quantiles of a test statistic
rRendata                Simulate a random RenData object
readXML                 Read data using an XML index file
roundPred               Round quantiles in a pseudo-prediction table
skip2noskip             Fix non-skipped periods from skipped ones
spacings                Methods computing spacings between Largest
                        Order Statistics
summary.Rendata         Summary and print methods for "Rendata" objects
summary.Renouv          Summary and print methods for "Renouv" objects
translude               Make translucient colors
vcov.Renouv             Variance-covariance matrix of the estimates of
                        a "Renouv" object
weibplot                Classical Weibull distribution plot

This package contains a function Renouv to fit "renouvellement" models.

Author(s)

Yves Deville <[e-mail]>, Lise Bardet <[e-mail]>

Maintainer: Yann Richet <[e-mail]>

References

• Miquel J. (1984) Guide pratique d'estimation des probabilités de crues, Eyrolles (coll. EDF DER).

• Coles S. (2001) Introduction to Statistical Modelling of Extremes Values, Springer.

• Embrechts P., Klüppelberg C. and Mikosch T. (1997) Modelling Extremal Events for Insurance and Finance. Springer.

See Also

The CRAN packages evd, ismev, extRemes, POT.

Examples

## 'Garonne' data set
summary(Garonne)
plot(Garonne)

## Weibull excesses
fG <- Renouv(x = Garonne,
             threshold = 3000,
             distname.y = "weibull",
             main = "Weibull fit for 'Garonne'")

coef(fG)
vcov(fG)
summary(fG)
logLik(fG)
## Re-plot if needed
plot(fG)

## Classical 'predict' method with usual formal args 
predict(fG, newdata = c(100, 150, 200), level = c(0.8, 0.9))