wrapper.EPI {ExtrPatt}

Wrapper function

Description

Handles all steps for estimation of EPI from raw-data: 1) Preprocessing into Frechet-Margins 2) Estimation of TPDM 3) Calculation of Principal Components 4) Estimation of EPI

Usage

wrapper.EPI(
  X,
  Y = NULL,
  q = 0.98,
  anz_cores = 1,
  clust = NULL,
  m = 1:10,
  thr_EPI = NULL
)

Arguments

X

A t x n dimensional Data-matrix with t: Number of time steps and n: Number of grid points/stations

Y

Optional: Sames as X but for second variable: If Y!=NULL, cross-TPDM instead of TPDM and SVD instead of PCA is computed

q

Threshold for computation of TPDM. Only data above the 'q'-quantile will be used for estimation. Choose such that 0 < q < 1.

anz_cores

Number of cores for parallel computing (default: 5)

clust

Optional_ Uf clust = NULL, no declustering is performed. Else, declustering according to cluster-length 'clust'

m

Numeric vector: Containing the principal components/expansion coefficients (in case of Y!=NULL) from which the EPI shall be computed (default: modes = c(1:10), calculates the EPI on first ten principle Components)

thr_EPI

Only if Y!=NULL: Threshold for computation of TEPI. Expansion-coefficients that exceed the 'q'-quantile will be used for estimation. Choose such that 0 < q < 1.

Value

In case of Y =NULL: A list containing:

• basis: The Eigenvectors of TPDM

• pc: The principal components of TPDM

• extremal.basis: The Eigenvectors of TPDM but transformed in positive reals with trans

• EPI: Extremal pattern index

In case of Y !=NULL: A list containing:

• U, V: The left- and right singular Vectors of cross-TPDM

• extr.U, extr.V: The left- and right singular vectors of cross-TPDM, but transformed in positive reals with trans

• pcU, pcV: The left- and right expansion coefficients of cross-TPDM

• EPI: Extremal pattern index

• TEPI: Threshold-based extremal pattern index

References

Szemkus & Friederichs 2023

Examples

data    <- precipGER

result  <- wrapper.EPI(data$pr, m = 1:50)

rbPal <- colorRampPalette(c('blue', 'white','red'))
Col <- rbPal(10)[as.numeric(cut(result$basis[,2],breaks = 10))]
plot(data$lat, data$lon,col=Col)
plot(data$date, result$EPI, type='l')