Frechet {ReIns} | R Documentation |
The Frechet distribution
Description
Density, distribution function, quantile function and random generation for the Fréchet distribution (inverse Weibull distribution).
Usage
dfrechet(x, shape, loc = 0, scale = 1, log = FALSE)
pfrechet(x, shape, loc = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qfrechet(p, shape, loc = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rfrechet(n, shape, loc = 0, scale = 1)
Arguments
x |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
shape |
Shape parameter of the Fréchet distribution. |
loc |
Location parameter of the Fréchet distribution, default is 0. |
scale |
Scale parameter of the Fréchet distribution, default is 1. |
log |
Logical indicating if the densities are given as |
lower.tail |
Logical indicating if the probabilities are of the form |
log.p |
Logical indicating if the probabilities are given as |
Details
The Cumulative Distribution Function (CDF) of the Fréchet distribution is equal to
for all
and
otherwise. Both
shape
and scale
need to be strictly positive.
Value
dfrechet
gives the density function evaluated in ,
pfrechet
the CDF evaluated in and
qfrechet
the quantile function evaluated in . The length of the result is equal to the length of
or
.
rfrechet
returns a random sample of length .
Author(s)
Tom Reynkens.
See Also
Examples
# Plot of the PDF
x <- seq(1,10,0.01)
plot(x, dfrechet(x, shape=2), xlab="x", ylab="PDF", type="l")
# Plot of the CDF
x <- seq(1,10,0.01)
plot(x, pfrechet(x, shape=2), xlab="x", ylab="CDF", type="l")