RegioWeissman: Quantile estimation: Weissman's extrapolation

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

Description

Estimation of the p-quantile based on multiple local Hill estimators and Weissman's extrapolation formula. We assume heavy-tail homogeneity, i.e., all local EVI's are the same.

Usage

RegioWeissman(x, j = 1, p, k, k.qu = 20, type = "evopt", alpha = 0.05)

Arguments

x	Vector or matrix of observations
j	The number of the target site, i.e., if j=2 the p-quantile of the second column of x is estimated.
p	The probability of interest; should be between 1-k_j/n_j and 1, where n_j is the sample length of the j-th column.
k	Number of relative excesses involved in the estimation of the extreme value index gamma. If k is missing, it will be set to k=floor(2*n^(2/3)), where n is the sample length of the vector x after removing missing values k=floor(2*n^(2/3)/d^(1/3)), where d is the number of columns of the matrix x and n the length of each column after removing missing values.
k.qu	Tuning parameter for estimation of empirical variance; only needed if type="opt".
type	Choose either "evopt" if extreme value dependent, "ind" if independent or "opt" for arbitrarily dependent components.
alpha	Confidence level for confidence interval.

Value

List of

• est Point estimate of p-quantile of column j

• CI the corresponding alpha-confidence interval

• EVI estimate of the extreme value index

• k tail sample size

• p a probability

• u.kn (n-k)-th largest observation, where n is the sample length at station j after removing missing values

• description a short description.

Examples

library("evd")
# sample observations of 75 years at one station:
x <- rgev(75, 0, 1, 0) # x is a vector
RegioWeissman(x=x, p=0.95)

x2 <- c(NA, NA, x[1:60], NA, x[61:75]) # vector of observations with missing values
RegioWeissman(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)
RegioWeissman(x=x, p=0.9, j=3)

# With missing values:
x2 <- x
x2[sample(100, 12),2] <- NA
RegioWeissman(x=x2, p=0.9, j=3)

Example output

$est
[1] 5.897141

$CI
[1]  0.8164773 10.9778039

$EVI
[1] 1.164289

$k
[1] 35

$p
[1] 0.95

$u.kn
[1] 0.4377618

$description
[1] "Quantile estimation method: Local Weissman extrapolation"

$est
[1] 5.897141

$CI
[1]  0.8164773 10.9778039

$EVI
[1] 1.164289

$k
[1] 35

$p
[1] 0.95

$u.kn
[1] 0.4377618

$description
[1] "Quantile estimation method: Local Weissman extrapolation"

$est
[1] 4.416041

$CI
[1] 4.118806 4.713276

$EVI
[1] 0.343242

$k
[1] 27 27 27 27

$p
[1] 0.9

$u.kn
[1] 3.140299

$description
[1] "Quantile estimation method: Regional Weissman extrapolation"

Warning messages:
1: In c(-1, 1) * gammaEst * qnorm(1 - alpha/2) * sqrt(t(w) %*% Sigma %*%  :
  Recycling array of length 1 in vector-array arithmetic is deprecated.
  Use c() or as.vector() instead.

2: In c(-1, 1) * qnorm(1 - alpha/2) * sqrt((w1$est^2 * w1$w %*% w1$Sigma %*%  :
  Recycling array of length 1 in vector-array arithmetic is deprecated.
  Use c() or as.vector() instead.

$est
[1] 4.399966

$CI
[1] 4.102435 4.697496

$EVI
[1] 0.3395703

$k
[1] 27 24 27 27

$p
[1] 0.9

$u.kn
[1] 3.140299

$description
[1] "Quantile estimation method: Regional Weissman extrapolation"

Warning messages:
1: In c(-1, 1) * gammaEst * qnorm(1 - alpha/2) * sqrt(t(w) %*% Sigma %*%  :
  Recycling array of length 1 in vector-array arithmetic is deprecated.
  Use c() or as.vector() instead.

2: In c(-1, 1) * qnorm(1 - alpha/2) * sqrt((w1$est^2 * w1$w %*% w1$Sigma %*%  :
  Recycling array of length 1 in vector-array arithmetic is deprecated.
  Use c() or as.vector() instead.

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