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

## Description

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

## Usage

 `1` ```specdens(fitted, main, plot = TRUE, ...) ```

## Arguments

 `fitted` 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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```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) ```

### Example output

```
```

POT documentation built on May 2, 2019, 7:30 a.m.