POT: bvretlev – R documentation

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POT

bvretlev

Return Level Plot: Bivariate Case

Description

Plot return levels for a fitted bivariate extreme value distribution.

Usage

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

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.

Details

Any bivariate extreme value distribution has the Pickands' representation form i.e.:

G(y1, y2) = exp( - (1/z1 + 1/z2) A(w) )

where zi corresponds to yi transformed to be unit Frechet distributed and w = z2 / (z1 + z2) which lies in [0,1].

Thus, for a fixed probability p and w, we have the corresponding z1, z2 values:

z1 = - A(w) / (w log(p))

z2 = z1 w / (1-w)

At last, the zi are transformed back to their original scale.

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.

Author(s)

Mathieu Ribatet

Examples

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

POT

Generalized Pareto Distribution and Peaks Over Threshold

v1.1-10

GPL (>= 2)

Authors

Mathieu Ribatet [aut], Christophe Dutang [ctb,cre]

Initial release