Description Usage Arguments Details Value References Examples
LogDensity function of the generalised extreme value (GEV) distribution
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x 
Numeric vectors of quantiles. 
loc, scale, shape 
Numeric scalars.
Location, scale and shape parameters.

It is assumed that x
, loc
= μ,
scale
= σ and shape
= ξ are such that
the GEV density is nonzero, i.e. that
1 + ξ (x  μ) / σ > 0. No check of this, or that
scale
> 0 is performed in this function.
The distribution function of a GEV distribution with parameters
loc
= μ, scale
= σ (>0) and
shape
= ξ is
F(x) = exp {  [1 + ξ (x  μ) / σ] ^ (1/ξ)}
for 1 + ξ (x  μ) / σ > 0. If ξ = 0 the distribution function is defined as the limit as ξ tends to zero. The support of the distribution depends on ξ: it is x <= μ  σ / ξ for ξ < 0; x >= μ  σ / ξ for ξ > 0; and x is unbounded for ξ = 0. Note that if ξ < 1 the GEV density function becomes infinite as x approaches μ σ / ξ from below.
See https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution for further information.
A numeric vector of value(s) of the logdensity of the GEV distribution.
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
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