gevdist {mev} | R Documentation |
Density function, distribution function, quantile function and random number generation for the generalized extreme value distribution.
qgev(p, loc = 0, scale = 1, shape = 0, lower.tail = TRUE, log.p = FALSE)
rgev(n, loc = 0, scale = 1, shape = 0)
dgev(x, loc = 0, scale = 1, shape = 0, log = FALSE)
pgev(q, loc = 0, scale = 1, shape = 0, lower.tail = TRUE, log.p = FALSE)
p |
vector of probabilities |
loc |
scalar or vector of location parameters whose length matches that of the input |
scale |
scalar or vector of positive scale parameters whose length matches that of the input |
shape |
scalar shape parameter |
lower.tail |
logical; if |
n |
scalar number of observations |
x , q |
vector of quantiles |
log , log.p |
logical; if |
The distribution function of a GEV distribution with parameters
loc
= \mu
, scale
= \sigma
and
shape
= \xi
is
F(x) = \exp\{-[1 + \xi (x - \mu) / \sigma] ^ {-1/\xi} \}
for 1 + \xi (x - \mu) / \sigma > 0
. If \xi = 0
the
distribution function is defined as the limit as \xi
tends to zero.
The quantile function, when evaluated at zero or one, returns the lower and upper endpoint, whether the latter is finite or not.
Leo Belzile, with code adapted from Paul Northrop
Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158-171. Chapter 3: doi:10.1002/qj.49708134804
Coles, S. G. (2001) An Introduction to Statistical Modeling of Extreme Values, Springer-Verlag, London. doi:10.1007/978-1-4471-3675-0_3