retlev.mcpot {POT} | R Documentation |
Return level plot for Markov chain POT models.
## S3 method for class 'mcpot': retlev(fitted, opy, exi, main, xlab, ylab, xlimsup, ...)
fitted |
A object of class ``uvpot'' . Most often, the
return of the fitgpd function. |
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 fitexi function. |
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, it is setted to 500. |
... |
Other arguments to be passed to the plot
function. |
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.
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
Ferro, C. and Segers, J. (2003). Inference for clusters of extreme values. Journal of the Royal Statistical Society B. 65: 545–556.
retlev
, retlev.uvpot
,
retlev.mcpot
, fitexi
data(ardieres) Mcalog <- fitmcgpd(ardieres[,"obs"], 5, "alog") retlev(Mcalog, opy = 990)