https://github.com/cran/ismev
Tip revision: abaab4d794bb062bba65629f6729bf61165ec4fd authored by Eric Gilleland on 14 July 2009, 00:00:00 UTC
version 1.39
version 1.39
Tip revision: abaab4d
gev.fit.Rd
\name{gev.fit}
\alias{gev.fit}
\title{Maximum-likelihood Fitting of the GEV Distribution}
\description{
Maximum-likelihood fitting for the generalized extreme value distribution,
including generalized linear modelling of each parameter.
}
\usage{
gev.fit(xdat, ydat = NULL, mul = NULL, sigl = NULL, shl = NULL,
mulink = identity, siglink = identity, shlink = identity,
muinit = NULL, siginit = NULL, shinit = NULL,
show = TRUE, method = "Nelder-Mead", maxit = 10000, \dots)
}
\arguments{
\item{xdat}{A numeric vector of data to be fitted.}
\item{ydat}{A matrix of covariates for generalized linear modelling
of the parameters (or \code{NULL} (the default) for stationary
fitting). The number of rows should be the same as the length
of \code{xdat}.}
\item{mul, sigl, shl}{Numeric vectors of integers, giving the columns
of \code{ydat} that contain covariates for generalized linear
modelling of the location, scale and shape parameters repectively
(or \code{NULL} (the default) if the corresponding parameter is
stationary).}
\item{mulink, siglink, shlink}{Inverse link functions for generalized
linear modelling of the location, scale and shape parameters
repectively.}
\item{muinit, siginit, shinit}{numeric of length equal to total number
of parameters used to model the location, scale or shape parameter(s),
resp. See Details section for default (NULL) initial values.}
\item{show}{Logical; if \code{TRUE} (the default), print details of
the fit.}
\item{method}{The optimization method (see \code{\link{optim}} for
details).}
\item{maxit}{The maximum number of iterations.}
\item{\dots}{Other control parameters for the optimization. These
are passed to components of the \code{control} argument of
\code{optim}.}
}
\details{
The form of the GEV used is that of Coles (2001) Eq (3.2). Specifically,
positive values of the shape parameter imply a heavy tail, and negative values
imply a bounded upper tail.
For non-stationary fitting it is recommended that the covariates
within the generalized linear models are (at least approximately)
centered and scaled (i.e.\ the columns of \code{ydat} should be
approximately centered and scaled).
Let m=mean(xdat) and s=sqrt(6*var(xdat))/pi. Then, initial values
assigend when 'muinit' is NULL are m - 0.57722 * s (stationary case).
When 'siginit' is NULL, the initial value is taken to be s, and when
'shinit' is NULL, the initial value is taken to be 0.1. When
covariates are introduced (non-stationary case), these same initial
values are used by default for the constant term, and zeros for all
other terms. For example, if a GEV( mu(t)=mu0+mu1*t, sigma, xi) is
being fitted, then the initial value for mu0 is m - 0.57722 * s, and
0 for mu1.
}
\value{
A list containing the following components. A subset of these
components are printed after the fit. If \code{show} is
\code{TRUE}, then assuming that successful convergence is
indicated, the components \code{nllh}, \code{mle} and \code{se}
are always printed.
\item{nllh}{single numeric giving the negative log-likelihood value.}
\item{mle}{numeric vector giving the MLE's for the location, scale and shape parameters, resp.}
\item{se}{numeric vector giving the standard errors for the MLE's for the location, scale and shape parameters, resp.}
\item{trans}{An logical indicator for a non-stationary fit.}
\item{model}{A list with components \code{mul}, \code{sigl}
and \code{shl}.}
\item{link}{A character vector giving inverse link functions.}
\item{conv}{The convergence code, taken from the list returned by
\code{\link{optim}}. A zero indicates successful convergence.}
\item{nllh}{The negative logarithm of the likelihood evaluated at
the maximum likelihood estimates.}
\item{data}{The data that has been fitted. For non-stationary
models, the data is standardized.}
\item{mle}{A vector containing the maximum likelihood estimates.}
\item{cov}{The covariance matrix.}
\item{se}{A vector containing the standard errors.}
\item{vals}{A matrix with three columns containing the maximum
likelihood estimates of the location, scale and shape parameters
at each data point.}
}
\references{
Coles, S., 2001. An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London, U.K., 208pp.
}
\seealso{\code{\link{gev.diag}}, \code{\link{optim}},
\code{\link{gev.prof}}}
\examples{
data(portpirie)
gev.fit(portpirie[,2])
}
\keyword{models}