pickdep {POT} | R Documentation |
The Pickands' Dependence Function
Description
Return and optionally plot the Pickands' dependence function.
Usage
pickdep(object, main, bound = TRUE, plot = TRUE, ...)
Arguments
object |
A object of class |
main |
May be missing. If present, the plot title. |
bound |
Logical. Should the perfect dependent and independent case bounds be plotted? |
plot |
Logical. Should the dependence function be plotted? |
... |
Optional parameters to be passed to the
|
Details
It is common to parametrize a bivariate extreme value distribution
according to the Pickands' representation (Pickands, 1981). That is,
if is any bivariate extreme value distribution, then it has
the following parametrization:
where are unit Frechet.
is the Pickands' dependence function. It has the following
properties:
-
is defined on [0,1];
-
;
-
;
-
is a convex function;
For two independent (unit Frechet) random variables,
;
For two perfectly dependent (unit Frechet) random variables,
.
Value
The function returns an invisible function: the Pickands' dependence function. Moreover, the returned object has an attribute which specifies the model for the bivariate extreme value distribution.
If plot = TRUE
, then the dependence function is plotted.
Author(s)
Mathieu Ribatet
References
Pickands, J. (1981) Multivariate Extreme Value Distributions Proceedings 43rd Session International Statistical Institute
Examples
x <- rbvgpd(1000, alpha = 0.9, model = "mix", mar1 = c(0,1,0.25),
mar2 = c(2,0.5,0.1))
Mmix <- fitbvgpd(x, c(0,2), "mix")
pickdep(Mmix)