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

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MathWorks Support Team on 20 Jan 2010
Commented: Image Analyst on 12 Oct 2021
I would like to perform a Monte Carlo simulation in MATLAB and would like to see an example for this.

MathWorks Support Team on 17 Jun 2021
Edited: MathWorks Support Team on 21 Jun 2021
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:
##### 2 CommentsShowHide 1 older comment
Image Analyst on 12 Oct 2021
@Sahar Jolini just call it a bunch of times and use the built-in std() function:
numTrials = 1000;
n = 1e6;
mypi = zeros(1, numTrials); % Preallocate space.
for k = numTrials
% Get an estimate for pi.
mypi(k) = approxpi(n);
end
% Get the standard deviation of those estimates:
sd = std(mypi);

Image Analyst on 12 Oct 2021
For what it's worth, I'm attaching three of my Monte Carlo demos.