R: Compute empirical survivals (S) and return periods (T)
SandT
R Documentation
Compute empirical survivals (S) and return periods (T)
Description
Compute the empirical survival values and the empirical return periods
at the observations of an object. These are used as plotting positions
in several plots.
The object containing the data, with class "Renouv" or
"Rendata".
points
Option for the computation of the plotting positions. When
points is set to "p", the p-points formula is
used with the selected value of a. This formula is used to
compute the survival from which the return period is computed. When
instead points is set to "H", Nelson's formula
is used to compute the return periods, the survival value still
being given by the p-points formula. When the data is
heterogeneous, i.e. when object contains MAX and/or
OTS data, Nelson's formula is used only to compute the return
periods of the upper slice of levels.
a
Parameter used in the interpolation formula for the inverse return
periods as in Hirsch and Stedinger (1987).
naive
Logical. When TRUE, naive plotting positions are used to
display MAX or OTS data. These can be defined only
when a main sample exists in object as a x.OT element.
For each MAX or OTS block, the positions use the
number of events predicted using the rate of events as estimated
from the main sample. When the main sample has a small durations,
such predictions are likely to be misleading.
Details
When the object contains historical information (MAX or
OTS), the computation is an adaptation Hirsch and Stedinger
(1987) for the Marked Process (MP) context. The original method is
devoted to block maxima and interpolates the survival values at the
thresholds which are computed first. For MP, the interpolation is
done for the inverse return periods, and the survival values are
deduced from those of the inverse return periods.
Nelson's formula provides unbiased estimates for the values of the
cumulative hazard H(x) at the order statistics, and thus
can be used to estimate the log-return periods as required on the
return level plot.
Value
A list with the following elements
x
Numeric vector containing the ordered values from all the available
sources in the object: main sample, historical periods either 'MAX' or
'OTS'.
group, groupNames
Integer and character vectors giving the source of the values in
x, in the same order of the values. For instance,
group[10] gives the group form which x[10] was
extracted, and the name of this group is groupNames[group[10]].
S, T
Numeric vectors of the same length as x and containing the
corresponding estimation of the survival value and of the return
period.
thresh, lambda.thresh, S.thresh, T.thresh
Vector of thresholds and the corresponding estimation for the event
rate, survival and return period. All the estimations are for
the threshold values. The value of T.thresh[i] for a threshold
thresh[i] results from a simple computation: divide the sum of
the durations for blocks with thresholds >= thresh[i] by the
number of events for these blocks.
seealso
The ppoints and Hpoints functions.
Warning
When using points = "H" the estimated values of the survival
returned in S and those for the return period T no
longer verify T=1/S/lambda, where lambda is the
estimated rate. In this case, the values in T should be used in
the return level plot, while the values in S should be used in
the PP-plot.
Author(s)
Yves Deville
References
The original method for block maxima is described in
Hirsch R.M. and Stedinger J.R.(1887) Plotting Positions
for Historical Floods and their precision. Water
Ressources Research, vol. 23, N. 4 pp. 715-727.
Millard S. and Neerchal N. (2001). Environmental
Statistics with S-Plus. CRC Press
The adaptation for the Marked Process context is
described in the Renext Computing Details
document.
Examples
## use an object with class "Rendata"
ST1 <- SandT(object = Garonne)
## basic return level plot
plot(ST1$T, ST1$x, col = ST1$group, log = "x")
## use an object with class "Renouv"
fit <- Renouv(x = Garonne, plot = FALSE)
ST2 <- SandT(object = fit)
plot(ST2$T, ST2$x, col = ST2$group, log = "x")
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/SandT.Rd_%03d_medium.png", width=480, height=480)
> ### Name: SandT
> ### Title: Compute empirical survivals (S) and return periods (T)
> ### Aliases: SandT
>
> ### ** Examples
>
> ## use an object with class "Rendata"
> ST1 <- SandT(object = Garonne)
> ## basic return level plot
> plot(ST1$T, ST1$x, col = ST1$group, log = "x")
> ## use an object with class "Renouv"
> fit <- Renouv(x = Garonne, plot = FALSE)
> ST2 <- SandT(object = fit)
> plot(ST2$T, ST2$x, col = ST2$group, log = "x")
>
>
>
>
>
> dev.off()
null device
1
>
providing 
.
