# mrlplot: Empirical Mean Residual Life Plot In evd: Functions for Extreme Value Distributions

 mrlplot R Documentation

## Empirical Mean Residual Life Plot

### Description

The empirical mean residual life plot.

### Usage

```mrlplot(data, tlim, pscale = FALSE, nt = max(100, length(data)), lty =
c(2,1,2), col = 1, conf = 0.95, main = "Mean Residual Life Plot",
xlab = "Threshold", ylab = "Mean Excess", ...)
```

### Arguments

 `data` A numeric vector. `tlim` A numeric vector of length two, giving the limits for the thresholds at which the mean residual life plot is evaluated. If `tlim` is not given, sensible defaults are used. `pscale` If `TRUE`, then the x-axis gives the threshold exceedance probability rather than the threshold itself. `nt` The number of thresholds at which the mean residual life plot is evaluated. `lty, col` Arguments passed to `matplot`. The first and last elements of `lty` correspond to the lower and upper confidence limits respectively. Use zero to supress. `conf` The (pointwise) confidence coefficient for the plotted confidence intervals. `main` Plot title. `xlab, ylab` x and y axis labels. `...` Other arguments to be passed to `matplot`.

### Details

The empirical mean residual life plot is the locus of points

{u,1/n_u ∑_{i=1}^{n_u} (x(i) - u)}

where x(1), …, x(n_u) are the n_u observations that exceed the threshold u. If the exceedances of a threshold u0 are generalized Pareto, the empirical mean residual life plot should be approximately linear for u > u0.

The confidence intervals within the plot are symmetric intervals based on the approximate normality of sample means.

### Value

A list with components `x` and `y` is invisibly returned. The components contain those objects that were passed to the formal arguments `x` and `y` of `matplot` in order to create the mean residual life plot.

### Author(s)

Stuart Coles and Alec Stephenson

`fpot`, `matplot`, `tcplot`
```mrlplot(portpirie)