RegioGEV: Regional (or local) parameter and quantile estimation

In flood: Statistical Methods for the (Regional) Analysis of Flood Frequency

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 (≥ 0).
rightrim	integer indicating upper trimming parameter (≥ 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=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

Example output

$quant
    0.95 
2.337426 

$param
        loc       scale       shape 
-0.07740334  0.93490937 -0.09636016 

$quant
    0.95 
2.337426 

$param
        loc       scale       shape 
-0.07740334  0.93490937 -0.09636016 

$quant
[1] 4.613905

$param
      loc     scale     shape 
2.0166910 0.9506437 0.1671492 

$w
[1] "wopt"

$quant
[1] 4.429501

$param
      loc     scale     shape 
2.0127047 0.8839010 0.1678164 

$w
[1] "wopt"

$quant
[1] 4.633086

$param
      loc     scale     shape 
2.0227444 0.9547153 0.1677913 

$w
[1] "wopt"

$quant
[1] 5.26908

$param
      loc     scale     shape 
1.9700307 1.0034084 0.3180654 

$w
[1] "w"

flood documentation built on May 2, 2019, 4:04 p.m.