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.: $G (y_{1}, y_{2}) = \exp [- (\frac{1}{z_{1}} + \frac{1}{z_{2}}) A (w)]$ 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.

Examples

Run this code

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

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