evd (version 1.2-3)

bvdp: A Dependence Function Plot for a Bivariate evd Object

Description

The dependence function for the fitted model is plotted and (optionally) compared to a non-parameteric estimate.

Usage

bvdp(x, method = "cfg", modify = 0, wf = function(t) t, add = FALSE,
    lty = 1, nplty = 2, blty = 3, main = "Dependence Function", 
    xlab = "", ylab = "", ...)

Arguments

x

An object of class "bvevd".

method,modify,wf

Arguments passed to abvnonpar, which calculates and plots non-parametric dependence function estimates.

add

Logical; add to an existing plot?

lty,nplty,blty

Line types; for the model estmate, the non-parametric estimate and the border respectively. Use zero to suppress.

main

Title of plot.

xlab,ylab

Labels for x and y axes.

...

Other plot parameters.

Details

Any bivariate extreme value distribution can be written as $$G(z_1,z_2) = \exp\left[-(y_1+y_2)A\left( \frac{y_1}{y_1+y_2}\right)\right]$$ for some function $A(\cdot)$ defined on $[0,1]$, where $$y_i = {1+s_i(z_i-a_i)/b_i}^{-1/s_i}$$ for $1 + s_i(z_i-a_i)/b_i > 0$ and $i = 1,2$, with the (generalized extreme value) marginal parameters given by $(a_i,b_i,s_i)$, $b_i > 0$.

$A(\cdot)$ is called (by some authors) the dependence function. It follows that $A(0) = A(1) = 1$, and that $A(\cdot)$ is a convex function with $\max(w,1-w) \leq A(w)\leq 1$ for all $0\leq w\leq1$. $A(\cdot)$ does not depend on the marginal parameters. For non-stationary models the data are transformed to stationarity. The plot then corresponds to the distribution obtained when all covariates are zero.

See Also

abvnonpar, abvlog, bvcpp, bvdens, plot.bvevd

Examples

bvdata <- rbvlog(100, dep = 0.6)
M1 <- fbvlog(bvdata)
bvdp(M1)