log_gev {chandwich}  R Documentation 
The Generalised Extreme Value LogDensity Function
Description
LogDensity 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 nonzero, 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 logdensity 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, 158171. Chapter 3: doi:10.1002/qj.49708134804
Coles, S. G. (2001) An Introduction to Statistical Modeling of Extreme Values, SpringerVerlag, London. doi:10.1007/9781447136750_3
Examples
log_gev(1:4, 1, 0.5, 0.8)
log_gev(1:3, 1, 0.5, 0.2)