Density function, distribution function, quantile function and random number generation for the generalized extreme value distribution.
Usage
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)Arguments
- 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
TRUE(default), returns the distribution function, otherwise the survival function- n
scalar number of observations
- x, q
vector of quantiles
- log, log.p
logical; if
TRUE, probabilities \(p\) are given as \(\log(p)\).
Details
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.
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. 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