MATLAB Answers

The Integration of Gaussian PDF to obtain the CDF why don’t I get the correct answer?

99 views (last 30 days)
I am trying to run a simulation, but before I do I wanted to write a simple program to ensure I could get a correct answer.
I start off by generating 10,000 long vector using a Normally distributed pseudorandom number generator (randn) with a mean =0 and sigma =1.
nsamples=100000; f=0 f=f+(1)*randn(nsamples,1);
x = f;
m = mean(f)
s = std(f)
I calculate the mean and std using the standard MATLAB functions (mean and std) verifying mean and sigma.
I then plot the data using the standard normal equation
where x is the RV, s=std deviation, and m is the mean.
I then integrate the PDF from -1 to 1 using the following commend
p1 = -.5 * ((x - m)/s) .^ 2;
p2 = (s * sqrt(2*pi));
G = exp(p1) ./ p2;
fun = @(x) G;
This generates another vector. So I calculate the mean of the CDF vector (cdfmean=mean(cdf)) and instead of getting something around 68% I get 56%


Sign in to comment.

Accepted Answer

Jonathan LeSage
Jonathan LeSage on 7 Nov 2013
After reviewing your code, I was able to figure out what was troubling you. The flow of your code and equations are all correct, however, you're making a small mistake when creating the normal distribution function (fun = @(x) G;).
Basically what is happening is that you have defined the variable x as a vector of random number already. These vector values are incorrectly used in p1, where x is supposed to be a function variable. As a result, G is just a constant vector. The output of a definite integral should be a scalar value in this case (around 68% as you mentioned) and not a vector.
Fortunately, the fix is quite straightforward, you just need to remove the definition of x as f and then fix your function. Here is how I would implement the integral:
% Generate normally distributed random numbers
nSamples = 100000;
f = 1*randn(nSamples,1);
% Compute normal distribution statistics
m = mean(f);
s = std(f);
% Define normal distribution and integrate over [-1,1] interval
normFun = @(x) 1/(sqrt(2*pi)*s)*exp(-(x-m).^2./(2*s^2));
cdf = integral(normFun,-1,1)
Hope this helps to clarify what was happening!


Sign in to comment.

More Answers (0)



Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!