View source: R/default-gen-retlev.R
retlev | R Documentation |
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.
retlev(object, ...) ## S3 method for class 'uvpot' retlev(object, npy, main, xlab, ylab, xlimsup, ci = TRUE, points = TRUE, ...) ## S3 method for class 'mcpot' retlev(object, opy, exi, main, xlab, ylab, xlimsup, ...)
object |
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 x-axis. 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
x-axis). 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 T-year 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 plotting-position 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.
prob2rp
, fitexi
.
#for uvpot class x <- rgpd(75, 1, 2, 0.1) pwmu <- fitgpd(x, 1, "pwmu") rl.fun <- retlev(pwmu) rl.fun(100) #for mcpot class data(ardieres) Mcalog <- fitmcgpd(ardieres[,"obs"], 5, "alog") retlev(Mcalog, opy = 990)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.