random variable with normal distribution
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how can i find the first five moments of a random variable with pdf gaussisn distribution , and finding the characteristic function all in matlab?
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Image Analyst
2020-12-22
编辑：Image Analyst
2020-12-22
To get a bunch of random numbers drawn from a normal distribution, use randn().
r = randn(...........
If you want the nth moment just take the nth root of the sum of the values and divide by the number of samples minus 1.
If you want the central moments, then subtract the mean before raising to a power.
Sounds like homework (so I didn't give the actual MATLAB code, which is actually pretty simple - just a single line of code). Is it homework?
7 个评论
saif yahya
2020-12-22
saif yahya
2020-12-22
Image Analyst
2020-12-22
Didn't they go over the formula in class? Here is some code including the Wikipedia definition:
fprintf('Beginning to run %s.m ...\n', mfilename);
% https://en.wikipedia.org/wiki/Moment_(mathematics)#Sample_moments
mu = 50;
sigma = 10;
numSamples = 1000000;
r = mu + sigma * randn(1, numSamples);
meanr = mean(r)
sdr = std(r)
histogram(r);
grid on;
xlabel('r')
ylabel('Count');
caption = sprintf('Mu = %.2f, SD = %.2f', mu, sigma);
title(caption);
% Find second moment
n = 2
mom = sum(r.^n) / (numSamples-1)
% Find second central moment
momCentral = sum((r - meanr).^n) / (numSamples-1)
fprintf('Done running %s.m ...\n', mfilename);
You simply need to put into a for loop over n and index the two moments by the loop index. Just add 2 lines of code and take one away. Beware than many universities employ plagiarism detectors.
saif yahya
2020-12-22
Image Analyst
2020-12-23
Use histogram() with the 'pdf' option to describe it numerically. Analytically it's the Gaussian function.
saif yahya
2020-12-23
Image Analyst
2020-12-23
histogram() will give you the actual, empirical pdf. Not some theoretical analytical function. So the values don't matter. Support doesn't matter. You get what the PDF actually IS.
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