RegioGEV {flood}

Regional (or local) parameter and quantile estimation

Description

Calculates regional (or local) parameters of a generalized extreme value (GEV) distribution using (trimmed) L-moments (see TLMoments and parameters) from a vector or matrix of observation. Based on these parameters, a p-quantile of the GEV will be calculated for the jth station.

Usage

RegioGEV(x, p, j = 1, leftrim = 0, rightrim = 0, na.rm = TRUE, ...)

Arguments

x

vector or matrix of observations (rows: observations, d columns: stations).

p

a probability.

j

quantile and parameter estimation for the jth station (jth column of x). Irrelevant if is x is a vector.

leftrim

integer indicating lower trimming parameter (\ge 0).

rightrim

integer indicating upper trimming parameter (\ge 0).

na.rm

Should missing values be removed?

...

additional arguments, see TLMoments.

Details

The optimal weights will be calculated as described in "Kinsvater, Fried and Lilienthal (2015): Regional extreme value index estimation and a test of tail homogeneity, Environmetrics, DOI: 10.1002/env.2376, Section 3.2". If it's not possible to calculate optimal weights (negative eigenvaules of an estimated covarinace matrix), simple weights will be calculated: w_j=\frac{n_j}{sum_{j=1}^d n_j}

Value

List of

• quant quantile calculation from an estimated GEV with a regional shape-parameter.

• param estimated parameter vector from a GEV (using L-moments or trimmed L-moments).

• w optimal or simple weighting (just returned if x is a matrix).

Examples

library("evd")
# sample observations of 75 years at one station:
x <- rgev(75) # x is a vector
RegioGEV(x=x, p=0.95)

x2 <- c(NA, NA, x[1:60], NA, x[61:75]) # vector of observations with missing values
RegioGEV(x=x2, p=0.95) # NAs will be removed

# sample observations of 100 years at 4 stations:
set.seed(1053)
x <- matrix(rgev(400, 2, 1, 0.3), ncol=4)
RegioGEV(x=x, p=0.9, j=3, leftrim=0, rightrim=0) # optimal weighting
RegioGEV(x=x, p=0.9, j=3, leftrim=0, rightrim=1) # optimal weighting

# With missing values:
x2 <- x
x2[c(54, 89, 300)] <- NA
RegioGEV(x=x2, p=0.9, j=3, leftrim=0, rightrim=0)

# sample again observations of 100 years at 4 stations:
set.seed(958)
x <- matrix(rgev(400, 2, 1, 0.3), ncol=4)
RegioGEV(x=x, p=0.9, j=3, leftrim=0, rightrim=0) # simple weighting