R: Parametric Spectral Density Functions of Bivariate Extreme...

hbvevd {evd} | R Documentation

## Parametric Spectral Density Functions of Bivariate Extreme Value Models

### Description

Calculate or plot the density h of the spectral measure H on the interval (0,1), for nine parametric bivariate extreme value models.

### Usage

    hbvevd(x = 0.5, dep, asy = c(1,1), alpha, beta, model = c("log", "alog",
        "hr", "neglog", "aneglog", "bilog", "negbilog", "ct", "amix"),
         half = FALSE, plot = FALSE, add = FALSE, lty = 1, ...)

### Arguments

`x` | A vector of values at which the function is evaluated (ignored if plot or add is `TRUE`). h(1/2) is returned by default.
`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, Coles-Tawn and asymmetric mixed models.
`model` | The specified model; a character string. Must be either `"log"` (the default), `"alog"`, `"hr"`, `"neglog"`, `"aneglog"`, `"bilog"`, `"negbilog"`, `"ct"` or `"amix"` (or any unique partial match), for the logistic, asymmetric logistic, Husler-Reiss, negative logistic, asymmetric negative logistic, bilogistic, negative bilogistic, Coles-Tawn and asymmetric mixed 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.
`half` | Logical; if `TRUE` the function is divided by two, corresponding to a spectral measure with total mass one rather than two.
`plot` | Logical; if `TRUE` the function is plotted. The x and y values used to create the plot are returned invisibly.
`add` | Logical; add to an existing plot?
`lty` | Line type.
`...` | Other high-level graphics parameters to be passed to `plot`.

### Details

Any bivariate extreme value distribution can be written as

G(z1,z2) = exp{-\int_0^1 max(w y1, (1-w) y2) H(dw)}

for some function H() defined on [0,1], satisfying

\int_0^1 w H(dw) = int_0^1 (1-w) H(dw) = 1.

In particular, the total mass of H is two. The functions y1 and y2 are as defined in `abvevd`.

H is called the spectral measure, with density h on the interval (0,1).

### Value

`hbvevd` calculates or plots the spectral density function h for one of nine parametric bivariate extreme value models, at specified parameter values.

### Point Masses

For differentiable models H may have up to two point masses: at zero and one. Assuming that the model parameters are in the interior of the parameter space, we have the following. For the asymmetric logistic and asymmetric negative logistic models the point masses are of size `1-asy1` and `1-asy2` respectively. For the asymmetric mixed model they are of size `1-alpha-beta` and `1-alpha-2*beta` respectively. For all other models the point masses are zero.

At independence, H has point masses of size one at both zero and one. At complete dependence [a non-differentiable model] H has a single point mass of size two at 1/2. In either case, h is zero everywhere.

### See Also

`abvevd`, `fbvevd`, `rbvevd`, `plot.bvevd`

### Examples

    hbvevd(dep = 2.7, model = "hr")
    hbvevd(seq(0.25,0.5,0.75), dep = 0.3, asy = c(.7,.9), model = "alog")
    hbvevd(alpha = 0.3, beta = 1.2, model = "negbi", plot = TRUE)

    bvdata <- rbvevd(100, dep = 0.7, model = "log")
    M1 <- fitted(fbvevd(bvdata, model = "log"))
    hbvevd(dep = M1["dep"], model = "log", plot = TRUE)

[Package evd version 2.3-4 Index]