MATLAB: Are there any examples showing how to perform Monte Carlo simulation in MATLAB

carloexamplesMATLABmontesimulation

I would like to perform a Monte Carlo simulation in MATLAB and would like to see an example for this.

Best Answer

Here is a simple example function which computes the value of pi by generating uniformly distributed points inside a square of side length 1 and determining the fraction of those points which fall inside the circle. Four times that fraction will be an approximation to pi.
function mypi = approxpi(n)
% Input: n = number of points to generate
%        Default is n = 1e6
%        Larger values of n should perform better
if nargin < 1
    n = 1e6;
end
% Generate uniformly distributed points in 
% [0, 1] x [0, 1]
xy = rand(n, 2); 
% Compute distance from (0.5, 0.5)
r = sqrt((xy(:,1)-0.5).^2+(xy(:,2)-0.5).^2); 
% Count fraction of points within 1/2 unit of (0.5, 0.5)
frac = sum(r <= 0.5) / n; 
% Since square has side 1, circle has radius (1/2) 
% and should have area of pi*(1/2)^2
% frac is approximately pi/4 so pi is approximately 4*frac
mypi = 4*frac;
Another example on Monte Carlo Simulation using MATLAB can be found at:
http://www.vertex42.com/ExcelArticles/mc/MatlabMCExample.html
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