Frechet function

The Frechet distribution

Density, distribution function, quantile function and random generation for the Fréchet distribution (inverse Weibull distribution). UTF-8

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 $\log(f)$, default is FALSE.
• lower.tail: Logical indicating if the probabilities are of the form $P(X\le x)$ (TRUE) or $P(X>x)$ (FALSE). Default is TRUE.
• log.p: Logical indicating if the probabilities are given as $\log(p)$, default is FALSE.

Details

The Cumulative Distribution Function (CDF) of the Fréchet distribution is equal to $F(x) = \exp(-((x-loc)/scale)^{-shape})$ for all $x \ge loc$ and $F(x)=0$ otherwise. Both shape and scale need to be strictly positive.

Returns

dfrechet gives the density function evaluated in $x$, pfrechet the CDF evaluated in $x$ and qfrechet the quantile function evaluated in $p$. The length of the result is equal to the length of $x$ or $p$.

rfrechet returns a random sample of length $n$.

Author(s)

Tom Reynkens.

See Also

tFréchet, Distributions

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")