trans | R Documentation |
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 class 'fevd'
trans(object, ..., burn.in = 499, return.all = FALSE)
object |
An R object with a |
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. |
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.
numeric vector of transformed data.
Eric Gilleland
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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