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Computing 4th cumulant of Gaussian variable

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Divij Gupta
Divij Gupta on 19 Jun 2021
Answered: Chunru on 19 Jun 2021
I am trying to write a program to compute the 4th cumulant for a given array of numbers. For a test, I'm generating an array of numbers distributed as a Gaussian distribution. The expected 4th order cumulant is 0. However, I am getting a wildly oscillating value, wildly oscillating around 0. Here is the code, I have no idea what is going wrong (if anything):
function cu4 = fourthCumulantReal(a)
cu4 = moment(a,4) - 3*(moment(a,2))^2;
end
Test Data: fourthCumulantReal(normrnd[0,1,[1,50]])

Answers (1)

Chunru
Chunru on 19 Jun 2021
When number of samples is sufficiently large, the sample mean (your fucntion output) is approaching to the true expected value (0).
fourthCumulantReal(normrnd(0,1,[1,500000]))
ans = -0.0036
function cu4 = fourthCumulantReal(a)
cu4 = moment(a,4) - 3*(moment(a,2))^2;
end

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