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\name{RtoDPQ.LC}
\alias{RtoDPQ.LC}
\title{Default procedure to fill slots d,p,q given r for Lebesgue decomposed distributions}
\description{
function to do get empirical density, cumulative distribution and quantile function from random numbers}
\usage{
RtoDPQ.LC(r, e = getdistrOption("RtoDPQ.e"),
n = getdistrOption("DefaultNrGridPoints"), y = NULL)
}
\arguments{
\item{r}{ the random number generator }
\item{e}{ \eqn{10^e} numbers are generated, a higher number leads to a better result. }
\item{n}{ The number of grid points used to create the approximated functions, a higher number leads to a better result.}
\item{y}{a (numeric) vector or \code{NULL}}
}
\details{
RtoDPQ.LC generates \eqn{10^e} random numbers, by default \deqn{e = RtoDPQ.e}.
Replicates are assumed to be part of the discrete part, unique values to be
part of the a.c. part of the distribution. For the replicated ones,
we generate a discrete distribution by a call to \code{\link{DiscreteDistribution}}.
For the a.c. part, similarly to \code{\link{RtoDPQ}} we have an optional parameter \code{y}
for using N. Horbenko's quantile trick: i.e.; on an equally spaced grid \code{x.grid} on [0,1], apply
\code{f(q(x)(x.grid))}, write the result to \code{y} and use these
values instead of simulated ones.
The a.c. density is formed on the basis of \eqn{n}
points using approxfun and density (applied to the unique values), by default \deqn{n = DefaultNrGridPoints}.
The cumulative distribution function is based on all random variables,
and, as well as the quantile function, is also created on the basis of \eqn{n} points using
\code{approxfun} and \code{ecdf}. Of course, the results are usually not exact as they rely on random numbers.}
\value{ \code{RtoDPQ.LC} returns an object of class \code{UnivarLebDecDistribution}.
}
\author{
Peter Ruckdeschel \email{peter.ruckdeschel@uni-oldenburg.de}}
\note{ Use \code{RtoDPQ} for absolutely continuous and \code{RtoDPQ.d} for discrete distributions. }
\seealso{
\code{\link{UnivariateDistribution-class}},
\code{\link{density}},
\code{\link{approxfun}},
\code{\link{ecdf}}}
\examples{
set.seed(20230508)
rn2 <- function(n)ifelse(rbinom(n,1,0.3),rnorm(n)^2,rbinom(n,4,.3))
x <- RtoDPQ.LC(r = rn2, e = 4, n = 512)
plot(x)
# returns density, cumulative distribution and quantile function of
# squared standard normal distribution
## IGNORE_RDIFF_BEGIN
d.discrete(x)(4)
## IGNORE_RDIFF_END
x2 <- RtoDPQ.LC(r = rn2, e = 5, n = 1024) # for a better result
plot(x2)
}
\keyword{math}
\keyword{distribution}
\keyword{arith}
\concept{random sample}
\concept{image distribution}
\concept{absolutely continuous distribution}
\concept{utility}
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