compute.EPI {ExtrPatt}

Estimation of EPI

Description

Estimates the extremal pattern index (EPI) from either the 'm' principle components after a PCA or left- and right expansion coefficients after an SVD. In case of a SVD, the threshold-based EPI (TEPI) can optionally be calculated.

Usage

compute.EPI(coeff, m = 1:10, q = 0.98)

Arguments

coeff

A list, containing the t x n dimensional principle components/expansion coefficients of TPDM. Can also be output of function 'est.tpdm'.

m

numeric vector: Containing the Principle Components from which EPI shall be computed (e.g. with modes = c(1:10), the EPI is calculated on first ten principle components)

q

Optional: A threshold for computation of TEPI

Details

Given the first 'm' modes of principle components u and eigenvalues after a PCA, the EPI is given as:

EPI_t^{u} = \sqrt{\sum_{k=1}^m (u_{t,k}^2)/\sum_{j=1}^m e_j}.

Given the first 'm' modes of expansion coefficients u and v and singular values e after a SVD, the EPI and TEPI are given as:

EPI_t^{u, v} = \sqrt{\sum_{k=1}^m (u_{t,k}^2 + v_{t,k}^2)/\sum_{j=1}^m e_j}.

TEPI_t^{u, v} = \sqrt{(\sum_{k=1}^m (u_{t,k}^2 + v_{t,k}^2)/\sum_{j=1}^m e_j) |_{(|u_{t,k}| > q_u , |v{t,k}| > q_v)}}.

Value

An array of length t, containing EPI. TEPI is computed if if q > 0.

References

Szemkus & Friederichs (2023)

Examples

data    <- precipGER

data.alpha2  <- to.alpha.2(data$pr)
Sigma   <- est.tpdm(data.alpha2,anz_cores =1)
res.pca <- pca.tpdm(Sigma, data.alpha2)
EPI <- compute.EPI(res.pca, m = 1:10)

plot(data$date, EPI, type='l')