Renext-package: 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 exceedances over the threshold to follow a probability distribution which can differ from the Generalised Pareto Distribution (GPD). Weibull or gamma exceedances are sometimes preferred to GPD exceedances. The special case of exponential exceedances (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 exceedances, or "OT data", and is always be required (for this version). 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 datacorrespond to the case where one knows the$r$largest observations over each block. The number$r$of may vary between 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 aperception threshold.

Historical data are often available in hydrology (e.g. for river flows) for 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 that the event dates are 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{Surete} Nucléaire{Nucleaire} (IRSN). The package is a non-academic tool designed for applied analysis on case studies and investigations or comparisons on classical probabilistic models. Additional information and material related to this package can be found at the URL https://gforge.irsn.fr/gf/project/renext.

Arguments

encoding

UTF-8

Details

ll{ Package: Renext Type: Package Version: 2.1-0 Date: 2013-10-03 License: GPL (>= 2) LazyLoad: yes } This package contains a function Renouv to fit "renouvellement" models.

References

Miquel J. (1984)Guide pratique d'estimation des probabilités{probabilites} de crues, Eyrolles (coll. EDF DER)
Coles S. (2001)Introduction to Statistical Modelling of Extremes Values, Springer.

Examples

Run this code

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

## Weibull exceedances
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))