| log_gev {chandwich} | R Documentation |
The Generalised Extreme Value Log-Density Function
Description
Log-Density function of the generalised extreme value (GEV) distribution
Usage
log_gev(x, loc = 0, scale = 1, shape = 0)
Arguments
x |
Numeric vectors of quantiles. |
loc, scale, shape |
Numeric scalars.
Location, scale and shape parameters.
|
Details
It is assumed that x, loc = \mu,
scale = \sigma and shape = \xi are such that
the GEV density is non-zero, i.e. that
1 + \xi (x - \mu) / \sigma > 0. No check of this, or that
scale > 0 is performed in this function.
The distribution function of a GEV distribution with parameters
loc = \mu, scale = \sigma (>0) 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 support of the distribution depends on \xi: it is
x <= \mu - \sigma / \xi for \xi < 0;
x >= \mu - \sigma / \xi for \xi > 0;
and x is unbounded for \xi = 0.
Note that if \xi < -1 the GEV density function becomes infinite
as x approaches \mu -\sigma / \xi from below.
See https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution for further information.
Value
A numeric vector of value(s) of the log-density of the GEV distribution.
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
Examples
log_gev(1:4, 1, 0.5, 0.8)
log_gev(1:3, 1, 0.5, -0.2)