Method function to transform a data set. In the case of fevd objects, the transformation is to a standardized Gumbel or exponential scale.
trans(object, ...)# S3 method for fevd
trans(object, ..., burn.in = 499, return.all = FALSE)
numeric vector of transformed data.
An R object with a trans method. In the case of “fevd” objects, output from fevd.
number giving the burn in value. The first 1:burn.in will not be used in obtaining parmaeter estiamtes.
logical, only for POT models, but primarily for use with the Point Process model. Should only the threshold exceedances be returned?
Not used.
Eric Gilleland
Many important situations occur in extreme value analysis (EVA) where it is useful or necessary to transform data to a standardized scale. For example, when investigating multivariate or conditional EVA much of the theory revolves around first transfroming the data to a unit scale. Further, for non-stationary models, it can be useful to transform the data to a df that does not depend on the covariates.
The present function transforms data taken from “fevd” class objects and transforms them to either a standard Gumbel (GEV, Gumbel case) or standard exponential (GP, PP, exponential case) df. In the first case, if the data are Gumbel distributed (really, if a gumbel fit was performed) the transformation is:
z = (x - location(yi))/scale(yi),
where yi represent possible covariate terms and z is distributed according to a Gumbel(0, 1) df. If the data are GEV distributed, then the transformation is:
z = - log(1 + (shape(yi)/scale(yi) * (x - location(yi)))^(-1/shape(yi))),
and again z is distributed Gumbel(0, 1).
In the case of exponentially distributed data, the transformation is:
z = (x - threshold(yi))/scale(yi)
and z is distributed according to an exponential(1) df.
For GP distributed data, the transformation is:
z = -log((1 + (shape(yi)/scale(yi) * (x - threshold(yi))))^(-1/shape(yi))
where again z follows an exponential(1) df.
For PP models, the transformation is:
z = (1 + shape(yi)/scale(yi) * (x - threshold(yi)))^(-1/shape(yi))
and z is distributed exponential(1).
See Coles (2001) sec. 2.3.2 for more details.
Coles, S. (2001) An introduction to statistical modeling of extreme values, London, U.K.: Springer-Verlag, 208 pp.
revtrans.evd, fevd
data(PORTw)
fit <- fevd(TMX1, PORTw, location.fun=~AOindex, units="deg C")
fit
z <- trans(fit)
fevd(z)
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