% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/laplace.R
\name{laplace_lowercase}
\alias{laplace_lowercase}
\alias{dlaplacemix}
\alias{plaplacemix}
\alias{qlaplacemix}
\alias{rlaplacemix}
\alias{dlaplacemixgpd}
\alias{plaplacemixgpd}
\alias{qlaplacemixgpd}
\alias{rlaplacemixgpd}
\alias{dlaplacegpd}
\alias{plaplacegpd}
\alias{qlaplacegpd}
\alias{rlaplacegpd}
\title{Lowercase vectorized Laplace distribution functions}
\usage{
dlaplacemix(x, w, location, scale, log = FALSE)

plaplacemix(q, w, location, scale, lower.tail = TRUE, log.p = FALSE)

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

rlaplacemix(n, w, location, scale)

dlaplacemixgpd(
  x,
  w,
  location,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  log = FALSE
)

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

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

rlaplacemixgpd(n, w, location, scale, threshold, tail_scale, tail_shape)

dlaplacegpd(x, location, scale, threshold, tail_scale, tail_shape, log = FALSE)

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

qlaplacegpd(
  p,
  location,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

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

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

\item{location, 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 Laplace-kernel topics in this file.
}
\details{
These helpers vectorize the scalar Laplace and Laplace-plus-GPD routines for interactive R use.
They retain the same location-scale parameterization and the same splice definition as the
uppercase functions. Quantiles continue to use the scalar root-finding or piecewise logic rather
than a separate approximation.
}
\section{Functions}{
\itemize{
\item \code{dlaplacemix()}: Laplace mixture density (vectorized)

\item \code{plaplacemix()}: Laplace mixture distribution function (vectorized)

\item \code{qlaplacemix()}: Laplace mixture quantile function (vectorized)

\item \code{rlaplacemix()}: Laplace mixture random generation (vectorized)

\item \code{dlaplacemixgpd()}: Laplace mixture + GPD density (vectorized)

\item \code{plaplacemixgpd()}: Laplace mixture + GPD distribution function (vectorized)

\item \code{qlaplacemixgpd()}: Laplace mixture + GPD quantile function (vectorized)

\item \code{rlaplacemixgpd()}: Laplace mixture + GPD random generation (vectorized)

\item \code{dlaplacegpd()}: Laplace + GPD density (vectorized)

\item \code{plaplacegpd()}: Laplace + GPD distribution function (vectorized)

\item \code{qlaplacegpd()}: Laplace + GPD quantile function (vectorized)

\item \code{rlaplacegpd()}: Laplace + GPD random generation (vectorized)

}}
\examples{
w <- c(0.6, 0.3, 0.1)
loc <- c(0, 1, -2)
scl <- c(1, 0.9, 1.1)

# Laplace mixture
dlaplacemix(c(-1, 0, 1), w = w, location = loc, scale = scl)
rlaplacemix(5, w = w, location = loc, scale = scl)

}
\seealso{
\code{\link[=laplace_mix]{laplace_mix()}}, \code{\link[=laplace_MixGpd]{laplace_MixGpd()}}, \code{\link[=laplace_gpd]{laplace_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{gamma_lowercase}},
\code{\link{invgauss_lowercase}},
\code{\link{lognormal_lowercase}},
\code{\link{normal_lowercase}}
}
\concept{vectorized kernel helpers}
