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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/MC.hitormiss.R
\name{MC.hitormiss}
\alias{MC.hitormiss}
\title{Hit or Miss Monte Carlo integration}
\usage{
MC.hitormiss(
FUN = function(x) x - x^2,
n = ani.options("nmax"),
from = 0,
to = 1,
col.points = c("black", "red"),
pch.points = c(20, 4),
...
)
}
\arguments{
\item{FUN}{the function to be integrated}
\item{n}{number of points to be sampled from the Uniform(0, 1) distribution}
\item{from, to}{the limits of integration}
\item{col.points, pch.points}{colors and point characters for points which
``hit'' or ``miss'' the area under the curve}
\item{\dots}{other arguments passed to \code{\link{points}}}
}
\value{
A list containing \item{x1}{ the Uniform random numbers generated on
x-axis} \item{x2}{ the Uniform random numbers generated on y-axis}
\item{y}{ function values evaluated at \code{x1} } \item{n}{ number of
points drawn from the Uniform distribtion } \item{est}{ the estimated value
of the integral }
}
\description{
Integrate a function using the Hit-or-Miss Monte Carlo algorithm.
}
\details{
We compute the proportion of points hitting the area under the curve, and the
integral can be estimated by the proportion multiplied by the total area of
the rectangle (from xmin to xmax, ymin to ymax).
}
\note{
This function is for demonstration purpose only; the integral might be
very inaccurate when \code{n} is small.
\code{ani.options('nmax')} specifies the maximum number of trials.
}
\references{
Examples at \url{https://yihui.org/animation/example/mc-hitormiss/}
}
\seealso{
\code{\link{integrate}}, \code{\link{MC.samplemean}}
}
\author{
Yihui Xie
}
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