# exi: Estimates of the Extremal Index In evd: Functions for Extreme Value Distributions

## Description

Estimates of the extremal index.

## Usage

 `1` ```exi(data, u, r = 1, ulow = -Inf, rlow = 1) ```

## Arguments

 `data` A numeric vector, which may contain missing values. `u` A single value giving the threshold, unless a time varying threshold is used, in which case `u` should be a vector of thresholds, typically with the same length as `data` (or else the usual recycling rules are applied). `r` Either a postive integer denoting the clustering interval length, or zero, in which case the intervals estimator of Ferro and Segers (2003) is used and following arguments are ignored. By default the interval length is one. `ulow` A single value giving the lower threshold, unless a time varying lower threshold is used, in which case `ulow` should be a vector of lower thresholds, typically with the same length as `data` (or else the usual recycling rules are applied). By default there is no lower threshold (or equivalently, the lower threshold is `-Inf`). `rlow` A postive integer denoting the lower clustering interval length. By default the interval length is one.

## Details

If `r` is a positive integer the extremal index is estimated using the inverse of the average cluster size, using the clusters of exceedences derived from `clusters`. If `r` is zero, an estimate based on inter-exceedance times is used (Ferro and Segers, 2003).

If there are no exceedances of the threshold, the estimate is `NaN`. If there is only one exceedance, the estimate is one.

## Value

A single value estimating the extremal index.

## References

Ferro, C. A. T. and Segers, J. (2003) Inference for clusters of extreme values. JRSS B, 65, 545–556.

`clusters`, `exiplot`

## Examples

 ```1 2 3 4``` ```exi(portpirie, 4.2, r = 3, ulow = 3.8) tvu <- c(rep(4.2, 20), rep(4.1, 25), rep(4.2, 20)) exi(portpirie, tvu, r = 1) exi(portpirie, tvu, r = 0) ```

### Example output

``` 0.5384615
 0.8
 0.9402985
```

evd documentation built on May 1, 2019, 10:11 p.m.