Package 'extRemes' - What are R and CRAN?

24 devd
Value
independently noted later by meteorologist A. F. Jenkins (1955). It enjoys theretical support for
modeling maxima taken over large blocks of a series of data.
The generalized Pareo df is given by (Pickands, 1975)
PrX 0, scale > 0, and x > threshold. If shape = 0, then the GP
df is defined by continuity and becomes
F(x) = 1 - exp(-(x - threshold)/scale).
There is an approximate relationship between the GEV and GP df’s where the GP df is approximately
the tail df for the GEV df. In particular, the scale parameter of the GP is a function of the
threshold (denote it scale.u), and is equivalent to scale + shape*(threshold - location) where scale,
shape and location are parameters from the “equivalent” GE Vdf. Similar to the GEV df, the shape
parameter determines the tail behavior, where shape = 0 gives rise to the exponential df (light tail),
shape > 0 the Pareto df (heavy tail) and shape < 0 the Beta df (bounded upper tail at location -
scale.u/shape). Theoretical justification supports the use of the GP df family for modeling excesses
over a high threshold (i.e., y = x - threshold). It is assumed here that x, q describe x (not y = x -
threshold). Similarly, the random draws are y + threshold.
See Coles (2001) and Reiss and Thomas (2007) for a very accessible text on extreme value analysis
and for more theoretical texts, see for example, Beirlant et al. (2004), de Haan and Ferreira (2006),
as well as Reiss and Thomas (2007).
’devd’ gives the density function, ’pevd’ gives the distribution function, ’qevd’ gives the quantile
function, and ’revd’ generates random deviates for the GEV or GP df depending on the type argument.
Note
There is a similarity between the location parameter of the GEV df and the threshold for the GP df.
For clarity, two separate arguments are emplyed here to distinguish the two instead of, for example,
just using the location parameter to describe both.
Author(s)
Eric Gilleland
References
Beirlant, J., Goegebeur, Y., Teugels, J. and Segers, J. (2004) Statistics of Extremes: Theory and
Applications. Chichester, West Sussex, England, UK: Wiley, ISBN 9780471976479, 522pp.
Coles, S. (2001) An introduction to statistical modeling of extreme values, London, U.K.: Springer-
Verlag, 208 pp.
de Haan, L. and Ferreira, A. (2006) Extreme Value Theory: An Introduction. New York, NY, USA:
Springer, 288pp.
Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological
elements. Quart. J. R. Met. Soc., 81, 158–171.