retlev.bvpot | R Documentation |
Plot return levels for a fitted bivariate extreme value distribution.
## S3 method for class 'bvpot' retlev(object, p = seq(0.75,0.95,0.05), main, n = 5000, only.excess = FALSE, ...)
object |
An object of class |
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 |
... |
Other parameters to pass to the |
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.
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.
Mathieu Ribatet
fitbvgpd
, plot
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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