% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/glme.gev11.R
\name{glme.gev11}
\alias{glme.gev11}
\title{Generalized L-moments estimation for non-stationary GEV11 model}
\usage{
glme.gev11(
  xdat,
  ntry = 5,
  ftol = 1e-06,
  opt.choose = "nllh",
  pen = "beta",
  pen.choice = 1,
  mu = -0.55,
  std = 0.2,
  p = 6,
  c1 = 5,
  c2 = 2,
  c0 = 0.35,
  q = NULL,
  show = FALSE,
  init.rob = TRUE,
  glme.pre = NULL
)
}
\arguments{
\item{xdat}{A numeric vector of data to be fitted.}

\item{ntry}{Number of attempts for parameter estimation (default 5).}

\item{ftol}{Tolerance for convergence (default 1e-6).}

\item{opt.choose}{Selection criterion among the multi-start solutions:
"nllh" (default, penalized negative log-likelihood) or "gof"
(goodness-of-fit by the number-of-exceedances measure).}

\item{pen}{Type of penalty function: "norm", "beta" (default), "ms",
"park", "cannon", "cd", or "no".}

\item{pen.choice}{Choice number for penalty hyperparameters (default 1).
See \code{\link{glme.gev}} for the preset values. Set to NULL to use
\code{p, c1, c2} (beta) or \code{mu, std} (norm) directly.}

\item{mu}{Mean for normal penalty (default -0.55).}

\item{std}{Std for normal penalty (default 0.2).}

\item{p}{Shape for beta penalty (default 6).}

\item{c1}{Scaling for beta penalty (default 5).}

\item{c2}{Limit for beta penalty (default 2).}

\item{c0}{Half-width of the adaptive beta penalty support (default 0.35).}

\item{q}{Optional fixed second shape parameter for the beta penalty.}

\item{show}{If TRUE, prints the objective value of each try.}

\item{init.rob}{Use robust regression for the WLS initialization
(default TRUE).}

\item{glme.pre}{Deprecated (ignored). The WLS pre-estimate is always used.}
}
\value{
A list containing:
\itemize{
  \item para.glme - Proposed GLME estimates (mu0, mu1, sigma0, sigma1, xi).
  \item nllh.glme - Penalized negative log-likelihood of the solution.
  \item convergence - 0 if converged, 5 otherwise.
  \item pen, pen_pen.choice - Penalty method (and choice) used.
  \item p_q, c1_c2, c0_c1_c2 - (for beta) hyperparameters used.
  \item mu_std - (for norm) hyperparameters used.
  \item strup.org - WLSE by the Strupczewski method (\code{strup.para}).
  \item para.wls - Modified WLS estimates (\code{strup.mdfy}).
  \item para.gado - GN16 method estimates.
  \item lme.sta - Stationary L-moment estimates.
  \item para.lme - Pure L-moment estimates; returned only when
    \code{pen="no"} (then identical to para.glme). For other penalties
    use \code{\link{lme.gev11}} directly.
  \item precis - (only when \code{pen="no"}) precision of the L-moment
    equation solution.
  \item data - The input data (used by the plot method).
}
The object has class \code{"glme11"}; see \code{\link{GLmom-methods}}.
}
\description{
This function estimates parameters of the non-stationary GEV11 model
where mu(t) = mu0 + mu1*t and sigma(t) = exp(sigma0 + sigma1*t),
by the generalized method of L-moment estimation (GLME).

Starting from the WLS pre-estimate of \code{\link{strup.gev11}},
the penalized objective (generalized L-moment distance based on the
asymptotic covariance of the sample L-moments, plus penalty) is
minimized over (mu0, sigma0, xi) with mu1 and sigma1 held at their
pre-estimated values. With \code{pen="no"} the result equals the pure
L-moment method \code{\link{lme.gev11}} of Shin et al. (2025b).
}
\examples{
data(PhliuAgromet)
x <- PhliuAgromet$prec

\donttest{
# Estimate non-stationary GEV11 parameters
result <- glme.gev11(x, ntry = 5)
print(result$para.glme)  # Proposed GLME estimates
}

}
\references{
Shin, Y., Shin, Y., Park, J. & Park, J.-S. (2025). Generalized method of
L-moment estimation for stationary and nonstationary extreme value models.
arXiv preprint arXiv:2512.20385. \doi{10.48550/arXiv.2512.20385}

Shin, Y., Shin, Y. & Park, J.-S. (2025). Building nonstationary extreme value
model using L-moments. Journal of the Korean Statistical Society, 54, 947-970.
\doi{10.1007/s42952-025-00325-3}
}
\seealso{
\code{\link{glme.gev}} for stationary GEV estimation,
  \code{\link{lme.gev11}} for the pure L-moment method (no penalty),
  \code{\link{strup.gev11}} for the WLS pre-estimation,
  \code{\link{GN16.gev11}} for the GN16 method,
  \code{\link{quagev.NS}} for non-stationary quantile computation.
}
\author{
Yonggwan Shin, Seokkap Ko, Jihong Park, Yire Shin, Jeong-Soo Park
}
