POT (version 1.1-11)

retlev.bvpot: Return Level Plot: Bivariate Case

Description

Plot return levels for a fitted bivariate extreme value distribution.

Usage

# S3 method for bvpot
retlev(object, p = seq(0.75,0.95,0.05), main, n = 5000,
only.excess = FALSE, ...)

Value

Plot return levels for a fitted bivariate extreme value distribution. Moreover, an invisible list is return which gives the points used to draw the current plot.

Arguments

object

An object of class "bvpot". Most often, the return object of the fitbvgpd function.

p

A vector of probabilities for which return levels must be drawn.

main

The title of the graphic window. May be missing.

n

The number (default: 5000) of points needed to draw return levels lines.

only.excess

Logical. If FALSE (the default), all observations are plotted, otherwise, only exceedances above at least one of the two thresholds are plotted.

...

Other parameters to pass to the plot function.

Author

Mathieu Ribatet

Details

Any bivariate extreme value distribution has the Pickands' representation form i.e.: $$G(y_1, y_2) = \exp\left[ - \left(\frac{1}{z_1} + \frac{1}{z_2} \right) A( w ) \right]$$ where \(z_i\) corresponds to \(y_i\) transformed to be unit Frechet distributed and \(w = \frac{z_2}{z_1 + z_2}\) which lies in \([0,1]\).

Thus, for a fixed probability \(p\) and \(w\), we have the corresponding \(z_1\), \(z_2\) values: $$z_1 = - \frac{A(w)}{w \log(p)}$$ $$z_2 = \frac{z_1 w}{1 - w}$$

At last, the \(z_i\) are transformed back to their original scale.

See Also

fitbvgpd, plot

Examples

x <- rbvgpd(1000, alpha = 0.25, mar1 = c(0, 1, 0.25))
Mlog <- fitbvgpd(x, c(0, 0), "log")
retlev(Mlog)