Runs declustering of threshold exceedances

Formula: cluster = consecutive exceedances within gap r

Usage

Evdec(x, u, r)

Arguments

x

Time-ordered series.

u

Threshold.

r

Run length separating two clusters.

Value

List with cluster_max, cluster_id, n_clusters, theta, n_exceed, estimate, n, method.

Details

A cluster ends once r consecutive observations fall below the threshold. The cluster maxima are approximately independent, which is what makes a GPD fit to them legitimate; the extremal index is estimated by the runs estimator, number of clusters over number of exceedances.

References

Smith (1989), Statistical Science 4(4):367-377.

Examples

Evdec(x = c(1, 2, 3, 4, 5, 6, 7, 8), u = 5L, r = 5L)
#> $cluster_max
#> [1] 8
#> 
#> $cluster_id
#> [1] 0 0 0 0 0 1 1 1
#> 
#> $n_clusters
#> [1] 1
#> 
#> $theta
#> [1] 0.3333333
#> 
#> $n_exceed
#> [1] 3
#> 
#> $estimate
#> [1] 0.3333333
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "runs declustering of threshold exceedances"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"