Calculates the components required to calculate the value of the information
matrix test under the \(D\)-gaps model, using vector data input.
Called by dgaps_imt.
dgaps_imt_stat(data, theta, u, D = 1, inc_cens = TRUE)A numeric vector of raw data. Missing values are allowed, but
they should not appear between non-missing values, that is, they only be
located at the start and end of the vector. Missing values are omitted
using na.omit.
A numeric scalar. An estimate of the extremal index
\(\theta\), produced by dgaps.
A numeric scalar. Extreme value threshold applied to data.
A numeric scalar. The censoring parameter \(D\). Threshold
inter-exceedances times that are not larger than D units are
left-censored, occurring with probability
\(\log(1 - \theta e^{-\theta d})\),
where \(d = q D\) and \(q\) is the probability with which the
threshold \(u\) is exceeded.
A logical scalar indicating whether or not to include
contributions from right-censored inter-exceedance times, relating to the
first and last observations. See dgaps.
A list
relating the quantities given on pages 18-19 of
Suveges and Davison (2010). All but the last component are vectors giving
the contribution to the quantity from each \(D\)-gap, evaluated at the
input value theta of \(\theta\).
ldj the derivative of the log-likelihood with respect to \(\theta\) (the score)
Ij the observed information
Jj the square of the score
dj Jj - Ij
Ddj the derivative of Jj - Ij with respect
to \(\theta\)
n_dgaps the number of \(D\)-gaps that contribute to the log-likelihood.
Holesovsky, J. and Fusek, M. Estimation of the extremal index using censored distributions. Extremes 23, 197-213 (2020). doi:10.1007/s10687-020-00374-3