# cdf_ev: Reversed functions for several Extreme Value Distributions In lfstat: Calculation of Low Flow Statistics for Daily Stream Flow Data

## Description

As several Extreme Value distributions are parameterized for high extreme values, reversed functions for minima (e.g. low flow statistics) are derived. Reversing is done by fitting to the negated data (`-x`), subtracting probabilities from one (`1 - f`) and computing the negated probabilities.

## Usage

 ```1 2 3``` ```cdf_ev(distribution, x, para) pel_ev(distribution, lmom, ...) qua_ev(distribution, f, para) ```

## Arguments

 `distribution` character vector of length one containing the name of the distribution. The family of the chosen distribution must be supported by the package lmom. See `lmom`. For example `distribution = "gev"` directly uses the functions from package lmom, whereas `distribution = "gevR"` performs reversing. `x` Vector of quantiles. `f` Vector of probabilities. `para` Numeric vector containing the parameters of the distribution, in the order zeta, beta, delta (location, scale, shape). `lmom` Numeric vector containing the L-moments of the distribution or of a data sample. E.g. as returned by `samlmu(x)`. `...` parameters like `bound`, passed on to the estimating function. E.g. in case of `dist = 'wei'` to `pelwei`.

## Value

cdf_ev gives the distribution function; qua_ev gives the quantile function.

`lmom`, `cdfgev`, `quagev`, `pelgev`.
 ``` 1 2 3 4 5 6 7 8 9 10``` ```data("ngaruroro") ng <- as.xts(ngaruroro) minima <- as.vector(apply.yearly(ng\$discharge, min, na.rm = TRUE)) # Weibull distribution and reversed GEV give the same results distr <- "wei" qua_ev(distr, seq(0, 1, 0.1), para = pel_ev(distr, samlmu(minima))) distr <- "gevR" qua_ev(distr, seq(0, 1, 0.1), para = pel_ev(distr, samlmu(minima))) ```