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.
SandT(object, points = c("p", "H"), a = 0, naive = FALSE)
A list with the following elements
Numeric vector containing the ordered values from all the available sources in the object: main sample, historical periods either 'MAX' or 'OTS'.
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]].
Numeric vectors of the same length as x and containing the
corresponding estimation of the survival value and of the return
period.
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.
The object containing the data, with class "Renouv" or
"Rendata".
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.
Parameter used in the interpolation formula for the inverse return periods as in Hirsch and Stedinger (1987).
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.
The ppoints and Hpoints functions.
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.
Yves Deville
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.
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.
## 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")
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