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.
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.
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)
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 0.0749 0.4205
## u = 80 86 0.0536 0.9545
## u = 90 57 0.0747 0.8842
## u = 100 39 0.1004 0.7901
## u = 110 31 0.0990 0.8927
## u = 120 24 0.1079 0.9147
## u = 130 22 0.1141 0.9061
## u = 140 18 0.1424 0.8099
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))
Davison A.C. and Smith R.L. (1990) “Models for Exceedances over High Thresholds” J.R. Statist. Soc. B (52) pp. 393-442.
Papastathopoulos I. and Tawn J.A. (2013) “Extended Generalized Pareto Models for Tail Estimation”, Journal of Statistical Planning and Inference (143), pp. 131-143.