evd (version 1.0-0)

bvdepfns: Dependence Functions for Bivariate Extreme Value Distributions

Description

Calculate or plot the dependence function for logistic, negative logistic and Husler-Reiss models.

Usage

abvalog(x = 0.5, dep, asy, plot = FALSE, border = TRUE, add = FALSE, 
    lty = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1), xlab = "", 
    ylab = "", ...) 
abvaneglog(x = 0.5, dep, asy, plot = FALSE, border = TRUE, add = FALSE, 
    lty = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1), xlab = "", 
    ylab = "", ...) 
abvhr(x = 0.5, dep, plot = FALSE, border = TRUE, add = FALSE, 
    lty = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1), xlab = "", 
    ylab = "", ...) 
abvlog(x = 0.5, dep, plot = FALSE, border = TRUE, add = FALSE, 
    lty = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1), xlab = "", 
    ylab = "", ...) 
abvneglog(x = 0.5, dep, plot = FALSE, border = TRUE, add = FALSE, 
    lty = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1), xlab = "", 
    ylab = "", ...)

Arguments

x

a vector values at which the dependence function is evaluated (ignored if plot is TRUE).

dep

dependence parameter.

asy

a vector containing two asymmetry parameters.

plot

logical; if TRUE the function is plotted and the values used to create the plot are returned invisibly.

border

logical; if TRUE a border representing the maximal domain is added to the plot.

add

logical; add to an existing plot?

lty, blty

function and border line types.

xlim, ylim

x and y-axis limits.

xlab, ylab

x and y-axis labels.

...

other high-level graphics parameters to be passed to plot.

Value

• abvlog and abvalog give the dependence function for the logistic and asymmetric logistic models respectively. abvneglog and abvaneglog give the dependence function for the negative logistic and asymmetric negative logistic models respectively. abvhr gives the dependence function for the Husler-Reiss model.

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 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 $\max(x,1-x) \leq A(x)\leq 1$ for all $0\leq x\leq1$. $A(\cdot)$ does not depend on the marginal parameters. $A(1/2)$ is returned by default since it is often a useful summary of dependence.

See Also

rbvalog, rbvaneglog, rbvhr, rbvlog, rbvneglog

Examples

abvhr(dep = 2.7)
abvalog(dep = .3, asy = c(.7,.9))
abvalog(seq(0,1,0.25), dep = .3, asy = c(.7,.9))