extRemes (version 2.0-9)

trans: Transform Data

Description

Method function to transform a data set. In the case of fevd objects, the transformation is to a standardized Gumbel or exponential scale.

Usage

trans(object, ...)
# S3 method for fevd
trans(object, ..., burn.in = 499, return.all = FALSE)

Arguments

object

An R object with a trans method. In the case of “fevd” objects, output from fevd.

burn.in

number giving the burn in value. The first 1:burn.in will not be used in obtaining parmaeter estiamtes.

return.all

logical, only for POT models, but primarily for use with the Point Process model. Should only the threshold exceedances be returned?

…

Not used.

Value

numeric vector of transformed data.

Details

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.

References

Coles, S. (2001) An introduction to statistical modeling of extreme values, London, U.K.: Springer-Verlag, 208 pp.

See Also

revtrans.evd, fevd

Examples

# NOT RUN {
data(PORTw)

fit <- fevd(TMX1, PORTw, location.fun=~AOindex, units="deg C")
fit

z <- trans(fit)

fevd(z)

# }