# simmcpot: Simulate an Markov Chain with a Fixed Extreme Value... In POT: Generalized Pareto Distribution and Peaks Over Threshold

## Description

Simulate a synthetic Markov chain from a fitted `'mcpot'` object.

## Usage

 `1` ```simmcpot(fitted, plot = TRUE, ...) ```

## Arguments

 `fitted` An object of class `'mcpot'`; most often the returned object of the `fitmcgpd` function. `plot` Logical. If `TRUE` (the default), the simulated Markov chain is plotted. `...` Other optional arguments to be passed to the `plot` function.

## Details

The simulated Markov chain is computed as follows:

1. Simulate a Markov chain `prob` with uniform margins on (0,1) and with the fixed extreme value dependence given by `fitted`;

2. For all `prob` such as prob <= 1 - pat, set mc = NA (where `pat` is given by `fitted\$pat`);

3. For all `prob` such as prob >= 1 - pat, set prob2 = (prob - 1 + pat) / pat. Thus, `prob2` are uniformly distributed on (0,1);

4. For all `prob2`, set ```mc = qgpd(prob2, thresh, scale, shape)```, where `thresh, scale, shape` are given by the `fitted\$threshold, fitted\$param["scale"]` and `fitted\$param["shape"]` respectively.

## Value

A Markov chain which has the same features as the fitted object. If `plot = TRUE`, the Markov chain is plotted.

## Author(s)

Mathieu Ribatet

`fitmcgpd`, `simmc`
 ```1 2 3 4 5 6 7 8 9``` ```data(ardieres) flows <- ardieres[,"obs"] Mclog <- fitmcgpd(flows, 5) par(mfrow = c(1,2)) idx <- which(flows <= 5) flows[idx] <- NA plot(flows, main = "Ardieres Data") flowsSynth <- simmcpot(Mclog, main = "Simulated Data") ```