R package Renextra

Goals

The Renextra R package has been financed by IRSN Behrig. It aims at enhancing the Renext package which is available on CRAN and on the IRSN GitHub public repos.

The present features of Renextra are

• Enhanced graphics relying on the ggplot2 package. The autoplot method and (to a lesser extend) autolayer method can be used to get standard plots as used in Peaks Over Threshold analyses, such as the return-level plot.

• S3 class RenouvTList for threshold choice and so-called threshold stability plot.

• Experimental implementation of the Extended Generalized Pareto Distribution EGPD3 of Papatatopoulos and Tawn (2013).

Note that the use of the EGPD3 distribution relies on the the general features of the Renext package, in which the distribution of the excesses over the threshold can be quite arbitrary. So, some initial values of the parameters must be given. The estimated values of the scale and shape parameters obtained by using the "GPD" distribution can be used along with kappa = 1.0, see the examples.

Installing

Provided that the remotes package is installed, the installation of Renextra using the giHub source can be obtained by

library(remotes)
install_github("https://github.com/IRSN/Renextra")

You can also select a specific branch or a specific commit by using the suitable syntax for install_github, see the remotes package documentation.

The package should soon be available in pre-compiled form (including
.zip a file for Windows) the Releases section.

Examples

Garonne (Jitterized)

The GaronneJit data object is a Rendata object derived from the Renouv objectRenext by jitterizing the observations

library(Renextra)
class(GaronneJit)

## [1] "Rendata"

autoplot(GaronneJit)

The object has class "Rendata" and describes both so-called systematic and historical observations. An autoplot method is made available for this class by Renextra.

When the object is used as the first argument of Renouv all the observations are used in the fit. Renextra adds an autoplot method for the "Renouv" class, producting a ggplot

fitGJ <- Renouv(GaronneJit, threshold = 3200, distname.y = "GPD", plot = FALSE)
autoplot(fitGJ)

Nidd River

The Nidd river example has been used in Davison and Smith (1990). The data are provided by the mev package. We fit using a standard Generalized Pareto for the excesses and then using an Exendended Generalized Pareto as in Papastathopoulos and Tawn (1013).

 library(mev)
 fit <- RenouvTList(nidd,
                    effDuration = 35,
                    threshold = seq(from =70, to = 140, by = 10),
                    distname.y = "GPD")
 summary(fit)

## RenouvTList object
## o Estimated coefficients
##         lambda         scale ind        shape         
## u =  70  3.943 [0.336] -0.989 [10.104]   0.323 [0.114]
## u =  80  2.457 [0.265] -2.213 [16.772]   0.343 [0.164]
## u =  90  1.629 [0.216] 12.104 [24.891]   0.238 [0.204]
## u = 100  1.114 [0.178] 50.288 [33.156]   0.003 [0.214]
## u = 110  0.886 [0.159] 64.108 [41.456]  -0.070 [0.240]
## u = 120  0.686 [0.140] 101.478 [49.078] -0.249 [0.238]
## u = 130  0.629 [0.134] 77.930 [57.890]  -0.142 [0.294]
## u = 140  0.514 [0.121] 98.568 [69.280]  -0.236 [0.322]
## o Kolmogorov-Smirnov test
##           n      D p.value
## u =  70 138 0.0750  0.4190
## u =  80  86 0.0536  0.9546
## u =  90  57 0.0751  0.8811
## u = 100  39 0.1012  0.7823
## u = 110  31 0.0994  0.8899
## u = 120  24 0.1079  0.9148
## u = 130  22 0.1138  0.9076
## u = 140  18 0.1405  0.8222

 autoplot(fit, show = list(quant = TRUE, allObs= TRUE))

 ## Threshold Stability with ECGPD3
 fitE <- RenouvTList(nidd,
                     effDuration = 35,
                     threshold = seq(from = 65.08, to = 88.61, len = 40),
                     start.par.y = c(scale = 30, shape = 0.0, kappa = 1.0),
                     distname.y = "EGPD3")
 autoplot(fitE, show = list(quant = TRUE, allObs= TRUE))

Note that since a large number of thresholds have been used the color scale is continuous rather than discrete as before.

By autoplotting the coefficients of a RenouvTList object we get hints on the threshold stability, especially regarding the shape coefficient.

 autoplot(coef(fitE, lambda = FALSE, sd = TRUE))

## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## suppression des ex-aequos de 'x'

References

Davison A.C. and Smith R.L. (1990) “Models for Exceedances over High Thresholds” J.R. Statist. Soc. B (52) pp. 393-442, doi.

Papastathopoulos I. and Tawn J.A. (2013) “Extended Generalized Pareto Models for Tail Estimation”, Journal of Statistical Planning and Inference (143), pp. 131-143, doi.