Renext (version 1.0-0)

Renext-package: Renewal method for extreme values extrapolation

Description

This package proposes fits and diagnostics for the so-called "renewal method", an alternative to other "Peaks Over Threshold" (POT) methods. The renewal method 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 (one dimensional) 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 will always be required. It can be completed with a second kind of data called historical data consisting in the largest observations over one or several periods called historical blocks. A third usable kind of information called unobserved levels occurs when a fixed level is known not to have been exceeded during a period with known duration. Historical data are often available in hydrology (e.g. 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 surete 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.

Details

ll{ Package: Renext Type: Package Version: 1.0-0 Date: 2010-06-10 License: GPL (>=2) LazyLoad: yes } This package contains functions fRenouv and rRenouv to fit or simulate from "renouvellement" models.

References

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

See Also

The packages evd, ismev, extRemes, bayesevd, POT.

Examples

## artificial data
test <- rRenouv(nb = 100, threshold = 40,
                par.N = list(lambda = 2),
                densfun.y = "weibull", par.y = mom2par("weibull", mean = 30, sd = 36))  

## exponential exceedances
fit.expon <- fRenouv(x.OT = test$x,
                     sumw.BOT = 100,
                     distname.y = "exponential",
                     threshold = 50,
                     conf.pct = c(70, 95, 99),
                     main = ""exponential" distr. (special)")