If prob is NULL (the default):
For stationary models the parameter names are loc, scale
and shape, for the location, scale and shape parameters
respectively.
For non-stationary models, the parameter names are loc,
locx1, …, locxn, scale and
shape, where x1, …, xn are the column names
of nsloc, so that loc is the intercept of the
linear model, and locx1, …, locxn
are the ncol(nsloc) coefficients.
If nsloc is a vector it is converted into a single column
data frame with column name trend, and hence the associated
trend parameter is named loctrend.
If \(\code{prob} = p\) is a probability:
The fit is performed using a different parameterization.
Let \(a\), \(b\) and \(s\) denote the location, scale
and shape parameters of the GEV distribution.
For stationary models, the distribution is parameterized
using \((z_p,b,s)\), where
$$z_p = a - b/s (1 - (-\log(1 - p))^s)$$
is such that \(G(z_p) = 1 - p\), where \(G\) is the
GEV distribution function.
\(\code{prob} = p\) is therefore the probability in the upper
tail corresponding to the quantile \(z_p\).
If prob is zero, then \(z_p\) is the upper end point
\(a - b/s\), and \(s\) is restricted to the negative
(Weibull) axis.
If prob is one, then \(z_p\) is the lower end point
\(a - b/s\), and \(s\) is restricted to the positive
(Frechet) axis.
The parameter names are quantile, scale
and shape, for \(z_p\), \(b\) and \(s\)
respectively.
For non-stationary models the parameter \(z_p\) is again given by
the equation above, but \(a\) becomes the intercept of the linear
model for the location parameter, so that quantile replaces
(the intercept) loc, and hence the parameter names are
quantile, locx1, …, locxn,
scale and shape, where x1, …, xn are
the column names of nsloc.
In either case:
For non-stationary fitting it is recommended that the covariates
within the linear model for the location parameter are (at least
approximately) centered and scaled (i.e.\ that the columns of
nsloc are centered and scaled), particularly if automatic
starting values are used, since the starting values for the
associated parameters are then zero.