extRemes (version 1.65)

extremalindex: Estimate the Extremal Index (theta)

Description

Estimates the extremal index based on the intervals estimator due to Ferro and Segers (2003).

Usage

extremalindex(xdat, u)

Arguments

xdat

numeric vector of the data.

u

User defined threshold. May be a single number or a numeric vector of same length as xdat.

Value

• A list with components:
• theta
  The intervals estimate of the extremal index (theta).
• msg
  A message stating whether any interexceedance times were above 2 and possibly other pertinent information.
• C
  The estimated number of clusters (handles ties).
• run.length
  The estimated run length for runs declustering.

Details

The extremal index is a useful indicator of how much clustering of exceedances of a threshold occurs in the limit of the distribution. If theta = 1, then the data is independent and if theta < 1, then there is some dependency (clustering) in the limit.

There are many possible estimators of the extremal index. The one used here is the intervals estimator described in Ferro and Segers (2003). It is unbiased in the mean and can be used to estimate the number of clusters, which is also done by this function.

References

Ferro, C. A. T. and Segers, J. (2003) Inference for clusters of extreme values. Journal of the Royal Statistical Society B, 65, (2), 545--556.

See Also

dclust

Examples

data( Tphap)
temp <- -Tphap[,"MinT"]
look <- extremalindex( temp, -70)
look