# specdens: Spectral Density Plot In POT: Generalized Pareto Distribution and Peaks Over Threshold

 specdens R Documentation

## Spectral Density Plot

### Description

Plot the spectral density for a bivariate extreme value distribution or an extreme Markov chain model.

### Usage

```specdens(object, main, plot = TRUE, ...)
```

### Arguments

 `object` An object of class `'bvpot'` or `'mcpot'`. Most often, the return object of the `fitbvgpd` or `fitmcgpd` function. `main` The title of the graphic window. May be missing. `plot` Logical. Should the spectral density be plotted? The default is to plot it. `...` Other options to be passed to the `plot` function.

### Details

Any bivariate extreme value distribution has the following representation:

G(z_1, z_2) = exp{ -int_0^1 max[q/z_1, (1-q)/z_2] dH(q)}

where H holds:

int_0^1 q dH(q) = int_0^1 (1-q) dH(q) = 1

H is called the spectral measure with density h. Thus, h is called the spectral density. In addition, H has a total mass of 2.

For two independent random variables, the spectral measure consists of two points of mass 1 at q=0,1. For two perfect dependent random variables, the spectral measure consists of a single point of mass 2 at q=0.5.

### Value

Plot the spectral density for a fitted bivariate extreme value distribution. Moreover, the spectral density is returned invisibly.

### Author(s)

Mathieu Ribatet

`retlev.bvpot`, `pickdep` and `plot.bvpot`

### Examples

```par(mfrow=c(1,2))
##Spectral density for a Markov Model
mc <- simmc(1000, alpha = 0.25, model = "log")
mc <- qgpd(mc, 0, 1, 0.1)
Mclog <- fitmcgpd(mc, 0, "log")
specdens(Mclog)
##Spectral density for a bivariate POT model
x <- rgpd(500, 5, 1, -0.1)
y <- rgpd(500, 2, 0.2, -0.25)
Manlog <- fitbvgpd(cbind(x,y), c(5,2), "anlog")
specdens(Manlog)
```

POT documentation built on April 14, 2022, 5:07 p.m.