% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/gamma.R
\name{gamma_lowercase}
\alias{gamma_lowercase}
\alias{dgammamix}
\alias{pgammamix}
\alias{qgammamix}
\alias{rgammamix}
\alias{dgammamixgpd}
\alias{pgammamixgpd}
\alias{qgammamixgpd}
\alias{rgammamixgpd}
\alias{dgammagpd}
\alias{pgammagpd}
\alias{qgammagpd}
\alias{rgammagpd}
\title{Lowercase vectorized gamma distribution functions}
\usage{
dgammamix(x, w, shape, scale, log = FALSE)

pgammamix(q, w, shape, scale, lower.tail = TRUE, log.p = FALSE)

qgammamix(
  p,
  w,
  shape,
  scale,
  lower.tail = TRUE,
  log.p = FALSE,
  tol = 1e-10,
  maxiter = 200
)

rgammamix(n, w, shape, scale)

dgammamixgpd(
  x,
  w,
  shape,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  log = FALSE
)

pgammamixgpd(
  q,
  w,
  shape,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

qgammamixgpd(
  p,
  w,
  shape,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE,
  tol = 1e-10,
  maxiter = 200
)

rgammamixgpd(n, w, shape, scale, threshold, tail_scale, tail_shape)

dgammagpd(x, shape, scale, threshold, tail_scale, tail_shape, log = FALSE)

pgammagpd(
  q,
  shape,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

qgammagpd(
  p,
  shape,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

rgammagpd(n, shape, scale, threshold, tail_scale, tail_shape)
}
\arguments{
\item{x}{Numeric vector of quantiles.}

\item{w}{Numeric vector of mixture weights.}

\item{shape, scale}{Numeric vectors (mix) or scalars (base+gpd) of component parameters.}

\item{log}{Logical; if \code{TRUE}, return log-density.}

\item{q}{Numeric vector of quantiles.}

\item{lower.tail}{Logical; if \code{TRUE} (default), probabilities are \eqn{P(X \le x)}.}

\item{log.p}{Logical; if \code{TRUE}, probabilities are on log scale.}

\item{p}{Numeric vector of probabilities.}

\item{tol, maxiter}{Tolerance and max iterations for numerical inversion.}

\item{n}{Integer number of observations to generate.}

\item{threshold, tail_scale, tail_shape}{GPD tail parameters (scalars).}
}
\value{
Numeric vector of densities, probabilities, quantiles, or random variates.
}
\description{
Vectorized R wrappers for the scalar gamma-kernel topics in this file.
}
\details{
These wrappers are vectorized interfaces to the scalar gamma and gamma-plus-GPD routines. They
preserve the package's shape-scale parameterization and the same splice definition used in the
fitted-model prediction code. Quantile wrappers delegate to the scalar inversion code rather than
implementing separate approximations.
}
\section{Functions}{
\itemize{
\item \code{dgammamix()}: Gamma mixture density (vectorized)

\item \code{pgammamix()}: Gamma mixture distribution function (vectorized)

\item \code{qgammamix()}: Gamma mixture quantile function (vectorized)

\item \code{rgammamix()}: Gamma mixture random generation (vectorized)

\item \code{dgammamixgpd()}: Gamma mixture + GPD density (vectorized)

\item \code{pgammamixgpd()}: Gamma mixture + GPD distribution function (vectorized)

\item \code{qgammamixgpd()}: Gamma mixture + GPD quantile function (vectorized)

\item \code{rgammamixgpd()}: Gamma mixture + GPD random generation (vectorized)

\item \code{dgammagpd()}: Gamma + GPD density (vectorized)

\item \code{pgammagpd()}: Gamma + GPD distribution function (vectorized)

\item \code{qgammagpd()}: Gamma + GPD quantile function (vectorized)

\item \code{rgammagpd()}: Gamma + GPD random generation (vectorized)

}}
\examples{
w <- c(0.55, 0.3, 0.15)
shp <- c(2, 4, 6)
scl <- c(1, 2.5, 5)

# Gamma mixture
dgammamix(c(1, 2, 3), w = w, shape = shp, scale = scl)
rgammamix(5, w = w, shape = shp, scale = scl)

# Gamma mixture + GPD
dgammamixgpd(c(2, 3, 4), w = w, shape = shp, scale = scl,
             threshold = 3, tail_scale = 0.9, tail_shape = 0.2)

# Gamma + GPD (single component)
dgammagpd(c(2, 3, 4), shape = 4, scale = 2.5, threshold = 3,
          tail_scale = 0.9, tail_shape = 0.2)

}
\seealso{
\code{\link[=gamma_mix]{gamma_mix()}}, \code{\link[=gamma_mixgpd]{gamma_mixgpd()}}, \code{\link[=gamma_gpd]{gamma_gpd()}}, \code{\link[=bundle]{bundle()}}, \code{\link[=get_kernel_registry]{get_kernel_registry()}}.

Other vectorized kernel helpers: 
\code{\link{amoroso_lowercase}},
\code{\link{base_lowercase}},
\code{\link{cauchy_mix_lowercase}},
\code{\link{invgauss_lowercase}},
\code{\link{laplace_lowercase}},
\code{\link{lognormal_lowercase}},
\code{\link{normal_lowercase}}
}
\concept{vectorized kernel helpers}
