pickdep | R Documentation |
Return and optionally plot the Pickands' dependence function.
pickdep(object, main, bound = TRUE, plot = TRUE, ...)
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
|
It is common to parametrize a bivariate extreme value distribution according to the Pickands' representation (Pickands, 1981). That is, if G is any bivariate extreme value distribution, then it has the following parametrization:
G(y_1, y_2) = exp[ -(1/z_1 + 1/z_2) A(z_2 / (z_1 + z_2))]
where z_i are unit Frechet.
A is the Pickands' dependence function. It has the following properties:
A is defined on [0,1];
A(0) = A(1) = 0;
max(w, 1-w) <= A(w) <= 1, for all w;
A is a convex function;
For two independent (unit Frechet) random variables, A(w) = 1, for all w;
For two perfectly dependent (unit Frechet) random variables, A(w) = max(w, 1-w).
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.
Mathieu Ribatet
Pickands, J. (1981) Multivariate Extreme Value Distributions Proceedings 43rd Session International Statistical Institute
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)
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