retlev.uvpot {POT} | R Documentation |
Return level plot for univariate POT models.
## S3 method for class 'uvpot': retlev(fitted, npy, main, xlab, ylab, xlimsup, ci = TRUE, points = TRUE, ...)
fitted |
A object of class ``uvpot'' . Most often, the
return of the fitgpd function. |
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 ``Return Level Plot''. |
xlab,ylab |
The labels for the x and y axis. If missing, they are set to ``Return Period (Years)'' and ``Return Level'' respectively. |
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 plot
function. |
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.
A graphical window. In addition, it returns invisibly the return level function.
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.
x <- rgpd(75, 1, 2, 0.1) pwmu <- fitgpd(x, 1, "pwmu") rl.fun <- retlev(pwmu) rl.fun(100)