MC.hitormiss: Hit or Miss Monte Carlo integration

In animation: A Gallery of Animations in Statistics and Utilities to Create Animations

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
n	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

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).

Value

A list containing

x1	the Uniform random numbers generated on x-axis
x2	the Uniform random numbers generated on y-axis
y	function values evaluated at x1
n	number of points drawn from the Uniform distribtion
est	the estimated value of the integral

Note

This function is for demonstration purpose only; the integral might be very inaccurate when n is small.

ani.options('nmax') specifies the maximum number of trials.

Author(s)

Yihui Xie

References

Examples at https://yihui.org/animation/example/mc-hitormiss/

See Also

integrate, MC.samplemean

animation documentation built on Oct. 7, 2021, 9:18 a.m.