Calculating cumulant from data set Given a data set x = <mo fence="false" stretchy="false">{

Brody Collins

Brody Collins

Answered question

2022-05-14

Calculating cumulant from data set
Given a data set x = { x ( n ) n = 1 , , m } how do I calculate the p t h -order cumulant? In particular I need to calculate the 4th-order cumulant. I found that I can calculate the cumulant from moments, but I also don't know how to calculate moments. I found how to calculate the 4th central moment (kurtosis) but I am not sure if/how they are related.
Since I have to implement the calculation of the cumulant in C++ I would be interested in a general explanation (to understand what I am doing) but also hints on how to implement the calculation efficiently would be appreciated. How can one interpret the 4th-order cumulant?
I am sorry if this is a trivial question but I don't have a strong mathematical background and was not able to find the answer online.

Answer & Explanation

necrologo9yh43

necrologo9yh43

Beginner2022-05-15Added 23 answers

The p-th order moment is given by
m p = 1 n k = 1 n x k p

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