% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/cauchy.R
\name{cauchy_mix_lowercase}
\alias{cauchy_mix_lowercase}
\alias{dcauchymix}
\alias{pcauchymix}
\alias{qcauchymix}
\alias{rcauchymix}
\title{Lowercase vectorized Cauchy mixture distribution functions}
\usage{
dcauchymix(x, w, location, scale, log = FALSE)

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

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

rcauchymix(n, w, location, scale)
}
\arguments{
\item{x}{Numeric vector of quantiles.}

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

\item{location, scale}{Numeric vectors 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.}
}
\value{
Numeric vector of densities, probabilities, quantiles, or random variates.
}
\description{
Vectorized R wrappers for the scalar Cauchy mixture functions in this file.
}
\details{
These are vectorized R wrappers around the scalar Cauchy-mixture routines.
They retain the same location-scale parameterization and the same inverse-CDF
logic for simulation and quantiles. The lowercase functions do not alter the
heavy-tail theory of the underlying Cauchy components; they apply the scalar
routines elementwise to vector inputs in R.
}
\section{Functions}{
\itemize{
\item \code{dcauchymix()}: Cauchy mixture density (vectorized)

\item \code{pcauchymix()}: Cauchy mixture distribution function (vectorized)

\item \code{qcauchymix()}: Cauchy mixture quantile function (vectorized)

\item \code{rcauchymix()}: Cauchy mixture random generation (vectorized)

}}
\examples{
w <- c(0.6, 0.3, 0.1)
loc <- c(-1, 0, 1)
scl <- c(1, 1.2, 2)

dcauchymix(c(-2, 0, 2), w = w, location = loc, scale = scl)
rcauchymix(5, w = w, location = loc, scale = scl)

}
\seealso{
\code{\link[=cauchy_mix]{cauchy_mix()}}, \code{\link[=cauchy]{cauchy()}}, \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{gamma_lowercase}},
\code{\link{invgauss_lowercase}},
\code{\link{laplace_lowercase}},
\code{\link{lognormal_lowercase}},
\code{\link{normal_lowercase}}
}
\concept{vectorized kernel helpers}
