kgaps_mle: Maximum likelihood estimation for the K-gaps model
In ConstantinosChr/exdex: Estimation of the Extremal Index

Description Usage Arguments Details Value References See Also Examples

Calculates maximum likelihood estimates of the extremal index θ based on the K-gaps model for threshold inter-exceedances times of Suveges and Davison (2010).

1	kgaps_mle(data, thresh, k = 1, inc_cens = FALSE, conf = NULL)

`data`	A numeric vector of raw data. No missing values are allowed.
`thresh`	A numeric scalar. Extreme value threshold applied to data.
`k`	A numeric scalar. Run parameter K, as defined in Suveges and Davison (2010). Threshold inter-exceedances times that are not larger than `k` units are assigned to the same cluster, resulting in a K-gap equal to zero. Specifically, the K-gap S corresponding to an inter-exceedance time of T is given by S = max(T - K, 0).
`inc_cens`	A logical scalar indicating whether or not to include contributions from censored inter-exceedance times relating to the first and last observation. See Attalides (2015) for details.
`conf`	A numeric scalar. If `conf` is supplied then a `conf`% likelihood-based confidence interval for θ is estimated.

The maximum likelihood estimate of the extremal index θ under the K-gaps model of Suveges and Davison (2010) is calculated. If inc_cens = TRUE then information from censored inter-exceedance times is included in the likelihood to be maximised, following Attalides (2015). The form of the log-likelihood is given in the Details section of kgaps_stats.

A list containing

theta_mle : The maximum likelihood estimate (MLE) of θ.
theta_se : The estimated standard error of the MLE.
theta_ci : (If conf is supplied) a numeric vector of length two giving lower and upper confidence limits for θ.
ss : The list of summary statistics returned from kgaps_stats.

Suveges, M. and Davison, A. C. (2010) Model misspecification in peaks over threshold analysis, The Annals of Applied Statistics, 4(1), 203-221. http://dx.doi.org/10.1214/09-AOAS292"

Attalides, N. (2015) Threshold-based extreme value modelling, PhD thesis, University College London. http://discovery.ucl.ac.uk/1471121/1/Nicolas_Attalides_Thesis.pdf

kgaps_stats for the calculation of sufficient statistics for the K-gaps model.

thresh <- quantile(newlyn, probs = 0.90)
# MLE and SE only
kgaps_mle(newlyn, thresh)
# MLE, SE and 95% confidence interval
kgaps_mle(newlyn, thresh, conf = 95)