Description Usage Arguments Details Value Warning Author(s) References See Also Examples
View source: R/defaultgenretlev.R
retlev
is a generic function used to show return level plot.
The function invokes particular methods
which depend on the class
of the first argument.
So the function makes a return level plot for POT models.
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fitted 
A fitted object. When using the POT package, an object
of class 
npy 
The mean Number of events Per Year (or more generally per block).if missing, setting it to 1. 
main 
The title of the graphic. If missing, the title is set to

xlab,ylab 
The labels for the x and y axis. If missing, they are
set to 
xlimsup 
Numeric. The right limit for the xaxis. If missing, a suited value is computed. 
ci 
Logical. Should the 95% pointwise confidence interval be plotted? 
points 
Logical. Should observations be plotted? 
... 
Other arguments to be passed to the 
opy 
The number of Observations Per Year (or more generally per block). If missing, it is set it to 365 i.e. daily values with a warning. 
exi 
Numeric. The extremal index. If missing, an estimate is
given using the 
For class "uvpot"
, the return level plot consists of plotting the theoretical quantiles
in function of the return period (with a logarithmic scale for the
xaxis). For the definition of the return period see the
prob2rp
function. Thus, the return level plot consists
of plotting the points defined by:
(T(p), F^{1}(p))
where T(p) is the return period related to the non exceedance probability p, F^{1} is the fitted quantile function.
If points = TRUE
, the probabilities p_j related to
each observation are computed using the following plotting position
estimator proposed by Hosking (1995):
p_j = (j  0.35) / n
where n is the total number of observations.
If the theoretical model is correct, the points should be “close” to the “return level” curve.
For class "mcpot"
, let X_1, …,X_n be the first n
observations from a stationary sequence with marginal distribution
function F. Thus, we can use the following (asymptotic)
approximation:
Pr[max{X_1,…,X_n} <= x] = [F(x)]^(n theta)
where theta is the extremal index.
Thus, to obtain the Tyear return level, we equate this equation to 1  1/T and solve for x.
A graphical window. In addition, it returns invisibly the return level function.
For class "mcpot"
, though this is computationally expensive, we recommend to give the
extremal index estimate using the dexi
function. Indeed,
there is a severe bias when using the Ferro and Segers (2003)
estimator  as it is estimated using observation and not the Markov
chain model.
Mathieu Ribatet
Hosking, J. R. M. and Wallis, J. R. (1995). A comparison of unbiased and plottingposition estimators of L moments. Water Resources Research. 31(8): 2019–2025.
Ferro, C. and Segers, J. (2003). Inference for clusters of extreme values. Journal of the Royal Statistical Society B. 65: 545–556.
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