abvpar {evd} | R Documentation

## Parametric Dependence Functions of Bivariate Extreme Value Models

### Description

Calculate or plot the dependence function A for eight parametric bivariate extreme value models.

### Usage

    abvpar(x = 0.5, dep, asy = c(1,1), alpha, beta, model = "log",
         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 or add is `TRUE`). A(1/2) is returned by default since it is often a useful summary of dependence.
`dep` | Dependence parameter for the logistic, asymmetric logistic, Husler-Reiss, negative logistic and asymmetric negative logistic models.
`asy` | A vector of length two, containing the two asymmetry parameters for the asymmetric logistic and asymmetric negative logistic models.
`alpha, beta` | Alpha and beta parameters for the bilogistic, negative bilogistic and Coles-Tawn models.
`model` | The specified model; a character string. Must be either `"log"` (the default), `"alog"`, `"hr"`, `"neglog"`, `"aneglog"`, `"bilog"`, `"negbilog"` or `"ct"` (or any unique partial match), for the logistic, asymmetric logistic, Husler-Reiss, negative logistic, asymmetric negative logistic, bilogistic, negative bilogistic and Coles-Tawn models respectively. The definition of each model is given in `rbvevd`. If parameter arguments are given that do not correspond to the specified model those arguments are ignored, with a warning.
`plot` | Logical; if `TRUE` the function is plotted. The x and y values used to create the plot are returned invisibly. If `plot` and `add` are `FALSE` (the default), the arguments following `add` are ignored.
`add` | Logical; add to an existing plot? The existing plot should have been created using either `abvpar` or `abvnonpar`, the latter of which plots (or calculates) a non-parametric estimate of the dependence function.
`lty, blty` | Function and border line types. Set `blty` to zero to omit the border.
`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`.

### Details

Any bivariate extreme value distribution can be written as

G(z1,z2) = exp{-(y1+y2)A[y1/(y1+y2)]}

for some function A() defined on [0,1], where

yi = {1+si(zi-ai)/bi}^(-1/si)

for 1+si(zi-ai)/bi > 0 and i = 1,2, with the (generalized extreme value) marginal parameters given by (ai,bi,si), bi > 0. If si = 0 then yi is defined by continuity.

A() is called (by some authors) the dependence function. It follows that A(0)=A(1)=1, and that A() is a convex function with max(x,1-x) <= A(x) <= 1 for all 0 <= x <= 1. The lower and upper limits of A are obtained under complete dependence and independence respectively. A() does not depend on the marginal parameters.

### Value

`abvpar` calculates or plots the dependence function for one of eight parametric bivariate extreme value models, at specified parameter values.

### See Also

`abvnonpar`, `fbvevd`, `rbvevd`, `atvpar`

### Examples

    abvpar(dep = 2.7, model = "hr")
    abvpar(seq(0,1,0.25), dep = 0.3, asy = c(.7,.9), model = "alog")
    abvpar(alpha = 0.3, beta = 1.2, model = "negbi", plot = TRUE)

    bvdata <- rbvevd(100, dep = 0.7, model = "log")
    M1 <- fitted(fbvevd(bvdata, model = "log"))
    abvpar(dep = M1["dep"], model = "log", plot = TRUE)
    abvnonpar(data = bvdata, add = TRUE, lty = 2)

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