Renext-package: Renewal Method for Extreme Values Extrapolation

In Renext: Renewal Method for Extreme Values Extrapolation

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

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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))

Renext documentation built on Aug. 30, 2023, 1:06 a.m.