exi {evd} | R Documentation

## Estimates of the Extremal Index

### Description

Estimates of the extremal index.

### Usage

    exi(data, u, r = 1, ulow = rep(-Inf, ncol(u)), rlow =
        rep(1, length(r)), dimnames = list(NULL, NULL), drop = TRUE)

### Arguments

`data` | A numeric vector, which may contain missing values.
`u` | A numeric vector of thresholds, unless time varying thresholds are used, in which case `u` should be a matrix, typically with `length(data)` rows (or else the usual recycling rules are applied).
`r` | A numeric vector of postive integers denoting the clustering interval lengths.
`ulow` | A numeric vector of lower thresholds with length `length(u)` (if `u` is a vector) or `ncol(u)` (if `u` is a matrix), unless time varying lower thresholds are used, in which case `ulow` should be a matrix with `length(u)` or `ncol(u)` columns, and typically with `length(data)` rows (or else the usual recycling rules are applied). By default there are no lower thresholds (or equivalently, the lower thresholds are `-Inf`).
`rlow` | A numeric vector of postive integers, of length `length(r)`, denoting the lower clustering interval lengths. The lower clustering interval length is only relevant if it is less than the clustering interval length and if there exists a lower threshold (greater than `-Inf`).
`dimnames` | The `dimnames` of the result.
`drop` | Logical; return a vector if either `u` or `r` has one element/column?

### Details

The extremal index is estimated using the inverse of the average cluster size, using the clusters of exceedences derived from `clusters`. If the threshold is larger than (or equal to) `max(data)`, so that no clusters are derived, then the corresponding estimate is `NaN`.

### Value

A matrix with `length(u)` (if `u` is a vector) or `ncol(u)` (if `u` is a matrix) rows and `length(r)` columns, such that the `ij`th element is the estimate of the extremal index using the threshold `u[i]` or `u[,i]`, the clustering interval length `r[j]`, the lower threshold `ulow[i]` or `ulow[,i]`, and the lower clustering interval length `rlow[j]`. If `drop` is `TRUE` (the default), a numeric vector is returned in preference to a matrix with one row/column.

### See Also

`clusters`

### Examples

    data(portpirie)
    exi(portpirie, 4.2, 3, 3.8)
    us <- seq(3.9, 4.2, len = 10)
    exi(portpirie, us, 3)
    exi(portpirie, us, 1:3)
    tvu <- c(rep(4.2, 20), rep(4.1, 25), rep(4.2, 20))
    exi(portpirie, as.matrix(tvu), 1:3)

    us <- seq(3.9, 4.2, len = 100)
    eis <- exi(portpirie, us, 1:3)
    matplot(us, eis, type = "l", xlab = "Threshold", ylab = "Ext. Index")

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