Density function, distribution function, quantile function and
random generation for the generalized extreme value (GEV)
distribution with location, scale and shape parameters.
dgev gives the density function, pgev gives the
distribution function, qgev gives the quantile function,
and rgev generates random deviates.
Arguments
x, q
Vector of quantiles.
p
Vector of probabilities.
n
Number of observations.
loc, scale, shape
Location, scale and shape parameters; the
shape argument cannot be a vector (must have length one).
log
Logical; if TRUE, the log density is returned.
lower.tail
Logical; if TRUE (default), probabilities
are P[X <= x], otherwise, P[X > x]
Details
The GEV distribution function with parameters
\(\code{loc} = a\), \(\code{scale} = b\) and
\(\code{shape} = s\) is
$$G(z) = \exp\left[-\{1+s(z-a)/b\}^{-1/s}\right]$$
for \(1+s(z-a)/b > 0\), where \(b > 0\).
If \(s = 0\) the distribution is defined by continuity.
If \(1+s(z-a)/b \leq 0\), the value \(z\) is
either greater than the upper end point (if \(s < 0\)), or less
than the lower end point (if \(s > 0\)).
The parametric form of the GEV encompasses that of the Gumbel,
Frechet and reverse Weibull distributions, which are obtained
for \(s = 0\), \(s > 0\) and \(s < 0\) respectively.
It was first introduced by Jenkinson (1955).
References
Jenkinson, A. F. (1955)
The frequency distribution of the annual maximum (or minimum) of
meteorological elements.
Quart. J. R. Met. Soc., 81, 158--171.