# gevrRl: GEVr Return Level Estimate and Confidence Interval for... In eva: Extreme Value Analysis with Goodness-of-Fit Testing

## Description

Computes stationary m-period return level estimate and interval, using either the delta method or profile likelihood.

## Usage

 ```1 2``` ```gevrRl(z, period, conf = 0.95, method = c("delta", "profile"), plot = TRUE, opt = c("Nelder-Mead")) ```

## Arguments

 `z` A class object returned from gevrFit. Must be a stationary fit. `period` The number of periods to use for the return level. `conf` Confidence level. Defaults to 95 percent. `method` The method to compute the confidence interval - either delta method (default) or profile likelihood. `plot` Plot the profile likelihood and estimate (vertical line)? `opt` Optimization method to maximize the profile likelihood if that is selected. The default method is Nelder-Mead.

## Details

It is generally accepted that profile likelihood confidence intervals provide greater accuracy than the delta method, in particular for large return level periods. Also, by their nature, delta method confidence intervals must be symmetric which may be undesirable for return level estimation. If the original fit was Gumbel, then return levels will be for the Gumbel distribution.

Caution: The profile likelihood optimization may be slow (on the order of minutes).

## Value

 `Estimate` Estimated m-period return level. `CI` Confidence interval for the m-period return level. `Period` The period length used. `ConfLevel` The confidence level used.

## References

http://www.mas.ncl.ac.uk/~nlf8/teaching/mas8391/background/chapter2.pdf

Coles, S. (2001). An introduction to statistical modeling of extreme values (Vol. 208). London: Springer.

## Examples

 ```1 2 3 4``` ```x <- rgevr(100, 2, loc = 0.5, scale = 1, shape = -0.3) z <- gevrFit(x) ## Compute 250-period return level. gevrRl(z, 250, method = "delta") ```

### Example output

```\$Estimate
[1] 2.532875

\$CI
[1] 2.114611 2.951139

\$Period
[1] 250

\$ConfLevel
[1] 0.95
```

eva documentation built on Oct. 18, 2018, 5:04 p.m.