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.
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 packages evd,
ismev,
extRemes,
bayesevd,
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))
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(Renext)
Loading required package: evd
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Renext/Renext-package.Rd_%03d_medium.png", width=480, height=480)
> ### Name: Renext-package
> ### Title: Renewal Method for Extreme Values Extrapolation
> ### Aliases: Renext-package Renext
> ### Keywords: datagen
>
> ### ** Examples
>
> ## 'Garonne' data set
> summary(Garonne)
o Dataset La Garonne river flow
data 'Garonne', variable 'Flow' (m3/s)
o OT data (main sample) from 1913-01-01 to 1978-01-01 (eff. dur. 65.00 years)
n Min. 1st Qu. Median Mean 3rd Qu. Max.
151 2530 2900 3200 3592 3995 7500
o no missing OT periods
o 'MAX' historical info: 1 blocks, 12 obs., total duration = 143.09 years
o no 'OTS' historical data
> plot(Garonne)
>
> ## Weibull excesses
> fG <- Renouv(x = Garonne,
+ threshold = 3000,
+ distname.y = "weibull",
+ main = "Weibull fit for 'Garonne'")
>
> coef(fG)
lambda shape scale
1.550137 1.086658 1104.135520
> vcov(fG)
lambda shape scale
lambda 0.0228075246 0.0007082357 -1.597855
shape 0.0007082357 0.0057833653 4.514266
scale -1.5978548456 4.5142657386 8803.576236
> summary(fG)
o Main sample 'Over Threshold'
. Threshold 3000.00
. Effect. duration 65.00 years
. Nb. of exceed. 98
o Estimated rate 'lambda' for Poisson process (events): 1.55 evt/year.
o Distribution for exceedances y: "weibull", with 2 par. "shape", "scale"
o No transformation applied
o Coefficients
Estimate Std. Error t value
lambda 1.550137 0.15102160 10.26434
shape 1.086658 0.07604844 14.28903
scale 1104.135520 93.82737466 11.76773
Degrees of freedom: 3 (param.) and 110 (obs)
o Inference method used for return levels
"Delta method"
o Return levels
period quant L.95 U.95 L.70 U.70
28 10 5793 5420 6165 5595 5990
32 20 6436 5964 6909 6187 6686
35 50 7272 6635 7909 6935 7609
37 100 7895 7114 8675 7482 8307
40 200 8510 7574 9446 8015 9005
42 300 8868 7837 9899 8322 9413
44 400 9120 8020 10221 8538 9702
45 500 9315 8160 10471 8704 9926
46 600 9475 8274 10675 8840 10110
48 700 9609 8369 10848 8953 10264
49 800 9725 8451 10998 9051 10398
50 900 9827 8524 11131 9138 10516
51 1000 9919 8588 11249 9215 10622
o 'MAX' historical info: 1 blocks, 12 obs., total duration = 143.09 years
* block 1, 143.09 years, 12 obs.
7500, 7400, 7000, 7000, 7000, 6600, 6500, 6500, 6400, 6300, 6300, 6200
o no 'OTS' historical data
o Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: OTjitter(y.OT, threshold = 0)
D = 0.12898, p-value = 0.07006
alternative hypothesis: two-sided
> logLik(fG)
[1] -856.4257
attr(,"df")
[1] 3
attr(,"nobs")
[1] 110
> ## 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))
period quant L.80 U.80 L.90 U.90
100 100 7894.567 7384.096 8405.039 7239.384 8549.751
150 150 8255.550 7686.549 8824.551 7525.245 8985.855
200 200 8510.365 7898.410 9122.319 7724.930 9295.799
>
>
>
>
>
> dev.off()
null device
1
>