MC.hitormiss: Hit or Miss Monte Carlo integration

Description

Integrate a function using the Hit-or-Miss Monte Carlo algorithm

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

FUN

the function to be integrated

number of points to be sampled from the Uniform(0, 1) distribution

from,to

the limits of integration

col.points,pch.points

colors and point characters for points which ``hit'' or ``miss'' the area under the curve

...

other arguments passed to points

Value

A list containing
x1the Uniform random numbers generated on x-axis
x2the Uniform random numbers generated on y-axis
yfunction values evaluated at x1
nnumber of points drawn from the Uniform distribtion
estthe estimated value of the integral

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).

References

http://animation.yihui.name/compstat:hit_or_miss_monte_carlo

Examples

Run this code

oopt = ani.options(interval = 0.2, nmax = ifelse(interactive(), 
    100, 2))

## should be close to 1/6
MC.hitormiss()$est

## should be close to 1/12
MC.hitormiss(from = 0.5, to = 1)$est

## HTML animation page
saveHTML({
    ani.options(interval = 0.5, nmax = ifelse(interactive(), 
        100, 2))
    MC.hitormiss()
}, img.name = "MC.hitormiss", htmlfile = "MC.hitormiss.html", 
    title = "Hit or Miss Monte Carlo Integration", description = c("", 
        "Generate Uniform random numbers", "and compute the proportion", 
        "of points under the curve."))

ani.options(oopt)

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