gev | R Documentation |
Density function, distribution function, quantile function and random generation for the generalized extreme value (GEV) distribution with location, scale and shape parameters.
dgev(x, loc=0, scale=1, shape=0, log = FALSE)
pgev(q, loc=0, scale=1, shape=0, lower.tail = TRUE)
qgev(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
rgev(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 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).
dgev
gives the density function, pgev
gives the
distribution function, qgev
gives the quantile function,
and rgev
generates random deviates.
Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158–171.
fgev
, rfrechet
,
rgumbel
, rrweibull
dgev(2:4, 1, 0.5, 0.8)
pgev(2:4, 1, 0.5, 0.8)
qgev(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
rgev(6, 1, 0.5, 0.8)
p <- (1:9)/10
pgev(qgev(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
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