dmev {mevr}

The Metastatistical Extreme Value Distribution

Description

Density, distribution function, quantile function and random generation for the MEV distribution with shape parameter 'w', scale parameter 'c'. Parameter 'n' refers either to the mean number of wet days per year in case of the simplified MEV, or to the number of wet days for each year.

Usage

dmev(x, w, c, n)

pmev(q, w, c, n)

qmev(p, w, c, n)

rmev(N, w, c, n)

Arguments

x, q

numeric vector or single values of quantiles for dmev and pmev.

w, c

vector or single values of shape and scale parameter of the MEV distribution. If a vector, w and c must have the same length as n.

n

Either mean number of wet events per year for the SMEV, or a vector for yearly MEVD calculations, i.e. one value per year (see details). If a vector, n must have the same length as w and c.

p

vector or single value of probabilities for qmev.

N

Number of observations to sample from the MEVD or SMEV.

Value

dmev gives the density function, pmev gives the distribution function, qmev gives the quantile function and rmev provides random realizations of the SMEV and MEVD.

Functions

• pmev(): distribution quantile function

• qmev(): quantile function

• rmev(): random generation function

Examples

# SMEV
dmev(1200:1300, 0.7, 20, 110)
pmev(1200:1300, 0.7, 70, 110)
qmev(1 - 1 / seq(5,50,5), 0.7, 70, 110)

# MEVD: 50-year event of 10 years Weibull series
w <- rnorm(10, 0.8, 0.1) # shape parameter
c <- rnorm(10, 200, 30) # scale parameter
n <- rnorm(10, 200, 50) # number of wet days
qmev(1 - 1 / 50, w, c, n)

# rl-plot
rp <- seq(5, 50, 5)
rl <- qmev(1 - 1 / rp, w, c, n)
pp <- (1:length(rp)) / (length(rp) + 1)
plot(pp, rl, type = "o")