# 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

 `1` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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) ```

flood documentation built on May 30, 2017, 8:25 a.m.