evd (version 1.2-3)

bvdepfns: Dependence Functions for Bivariate Extreme Value Distributions

Description

Calculate or plot the dependence function for the symmetric/asymmetric logistic, symmetric/asymmetric negative logistic, bilogistic, negative bilogistic, Husler-Reiss and Coles-Tawn models.

Usage

abvalog(x = 0.5, dep, asy = c(1, 1), plot = FALSE, add = FALSE,
    lty = 1, lwd = 1, col = 1, blty = 3, xlim = c(0, 1),
    ylim = c(0.5, 1), xlab = "", ylab = "", ...) 
abvaneglog(x = 0.5, dep, asy = c(1, 1), plot = FALSE, add = FALSE,
   lty = 1, lwd = 1, col = 1, blty = 3, xlim = c(0, 1),
   ylim = c(0.5, 1), xlab = "", ylab = "", ...) 
abvhr(x = 0.5, dep, plot = FALSE, add = FALSE, lty = 1, lwd = 1,
    col = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1), xlab = "", 
    ylab = "", ...) 
abvlog(x = 0.5, dep, plot = FALSE, add = FALSE, lty = 1, lwd = 1,
    col = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1), xlab = "", 
    ylab = "", ...) 
abvneglog(x = 0.5, dep, plot = FALSE, add = FALSE, lty = 1, lwd = 1,
    col = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1), xlab = "", 
    ylab = "", ...)
abvbilog(x = 0.5, alpha, beta, plot = FALSE, add = FALSE, lty = 1,
    lwd = 1, col = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1),
    xlab = "", ylab = "", ...) 
abvnegbilog(x = 0.5, alpha, beta, plot = FALSE, add = FALSE, lty = 1,
    lwd = 1, col = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1),
    xlab = "", ylab = "", ...)
abvct(x = 0.5, alpha, beta, plot = FALSE, add = FALSE, lty = 1,
    lwd = 1, col = 1, blty = 3, xlim = c(0, 1), ylim = c(0.5, 1),
    xlab = "", ylab = "", ...)

Arguments

x

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

dep

Dependence parameter.

asy

A vector containing two asymmetry parameters.

alpha, beta

Alpha and beta parameters.

plot

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

add

Logical; add to an existing plot?

lty, blty

Function and border line types. Use zero to suppress.

lwd

Line width.

col

Line colour.

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. abvct gives the dependence function for the Coles-Tawn model. abvbilog and abvnegbilog give the dependence function for the bilogistic and negative bilogistic models respectively.

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 $\max(x,1-x) \leq A(x)\leq 1$ 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

abvnonpar, bvdp, rbvalog, rbvaneglog, rbvhr, rbvlog, rbvneglog, rbvbilog, rbvnegbilog, rbvct

Examples

abvhr(dep = 2.7)
abvalog(dep = .3, asy = c(.7,.9))
abvalog(seq(0,1,0.25), dep = .3, asy = c(.7,.9))
abvnegbilog(alpha = .3, beta = 1.2, plot = TRUE)