retlev.mcpot {POT}R Documentation

Return Level Plot: Markov Chains Models

Description

Return level plot for Markov chain POT models.

Usage

## S3 method for class 'mcpot':
retlev(fitted, opy, exi, main, xlab, ylab, xlimsup,
...)

Arguments

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.

Details

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.

Value

A graphical window. In addition, it returns invisibly the return level function.

Warning

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.

Author(s)

Mathieu Ribatet

References

Ferro, C. and Segers, J. (2003). Inference for clusters of extreme values. Journal of the Royal Statistical Society B. 65: 545–556.

See Also

retlev, retlev.uvpot, retlev.mcpot, fitexi

Examples

data(ardieres)
Mcalog <- fitmcgpd(ardieres[,"obs"], 5, "alog")
retlev(Mcalog, opy = 990)

[Package POT version 1.0-9 Index]