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

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

Answer 1

[MathWorks Support Team]

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:

https://www.vertex42.com/ExcelArticles/mc/MatlabMCExample.html

[Image Analyst]

@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);

Answer 2

[Image Analyst]

For what it's worth, I'm attaching three of my Monte Carlo demos.