# qq: Quantile Quantile Plot In POT: Generalized Pareto Distribution and Peaks Over Threshold

## Description

`qq` is a generic function used to show quantile-quantile plot. The function invokes particular `methods` which depend on the `class` of the first argument. So the function makes a quantile quantile plot for univariate POT models.

## Usage

 ```1 2 3 4``` ```qq(fitted, ...) ## S3 method for class 'uvpot' qq(fitted, main, xlab, ylab, ci = TRUE, ...) ```

## Arguments

 `fitted` A fitted object. When using the POT package, an object of class `'uvpot'`. Most often, the return of the `fitgpd` function. `main` The title of the graphic. If missing, the title is set to `"QQ-plot"`. `xlab,ylab` The labels for the x and y axis. If missing, they are set to `"Model"` and `"Empirical"` respectively. `ci` Logical. If `TRUE` (the default), 95% intervals are plotted. `...` Other arguments to be passed to the `plot` function.

## Details

The quantile quantile plot consists of plotting the observed quantiles in function of the theoretical ones. The theoretical quantiles Q_{Theo, j} are computed from the fitted GPD, that is:

Q_{Theo, j} = F^{-1}(p_j)

where F^{-1} is the fitted quantile function and p_j are empirical probabilities defined by :

p_{j:n} = (j - 0.35) / n

where n is the total number of observations - see Hosking (1995).

If the theoretical model is correct, then points should be “near” the line y=x.

## Value

A graphical window.

Mathieu Ribatet

## References

Hosking, J. R. M. and Wallis, J. R. (1995). A comparison of unbiased and plotting-position estimators of L moments. Water Resources Research. 31(8): 2019–2025.

`qq`, `qq.uvpot`

## Examples

 ```1 2 3``` ```x <- rgpd(75, 1, 2, 0.1) pwmu <- fitgpd(x, 1, "pwmu") qq(pwmu) ```

### Example output

```
```

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