GenExtrVal {DescTools}  R Documentation 
The Generalized Extreme Value Distribution
Description
Density function, distribution function, quantile function and random generation for the generalized Extreme value (GenExtrVal) distribution with location, scale and shape parameters.
Usage
dGenExtrVal(x, loc=0, scale=1, shape=0, log = FALSE)
pGenExtrVal(q, loc=0, scale=1, shape=0, lower.tail = TRUE)
qGenExtrVal(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
rGenExtrVal(n, loc=0, scale=1, shape=0)
Arguments
x , q 
Vector of quantiles. 
p 
Vector of probabilities. 
n 
Number of observations. 
loc , scale , shape 
Location, scale and shape parameters; the

log 
Logical; if 
lower.tail 
Logical; if 
Details
The GenExtrVal distribution function with parameters
loc = a
, scale = b
and
shape = s
is
G(z) = \exp\left[\{1+s(za)/b\}^{1/s}\right]
for 1+s(za)/b > 0
, where b > 0
.
If s = 0
the distribution is defined by continuity.
If 1+s(za)/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 GenExtrVal 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).
Value
dGenExtrVal
gives the density function, pGenExtrVal
gives the
distribution function, qGenExtrVal
gives the quantile function,
and rGenExtrVal
generates random deviates.
Author(s)
Alec Stephenson <alec_stephenson@hotmail.com>
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.
See Also
rFrechet
,
rGumbel
, rRevWeibull
Examples
dGenExtrVal(2:4, 1, 0.5, 0.8)
pGenExtrVal(2:4, 1, 0.5, 0.8)
qGenExtrVal(seq(0.9, 0.6, 0.1), 2, 0.5, 0.8)
rGenExtrVal(6, 1, 0.5, 0.8)
p < (1:9)/10
pGenExtrVal(qGenExtrVal(p, 1, 2, 0.8), 1, 2, 0.8)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9