GenExtrVal {DescTools}  R Documentation 
Density function, distribution function, quantile function and random generation for the generalized Extreme value (GenExtrVal) distribution with location, scale and shape parameters.
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)
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 
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).
dGenExtrVal
gives the density function, pGenExtrVal
gives the
distribution function, qGenExtrVal
gives the quantile function,
and rGenExtrVal
generates random deviates.
Alec Stephenson <alec_stephenson@hotmail.com>
Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158–171.
rFrechet
,
rGumbel
, rRevWeibull
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