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I am trying to perform an analysis using the seventh moment but I can't seem to find an explicit formula for anything past the fourth moment.

  1. What is an explicit formula for the 7th moment similar to $\mu_1 =\frac{1}{N} \sum_i^N x_i$ for the mean ($1^{st}$ moment) and $\mu_2 =\frac{1}{N} \sum_i^N \left( x_i - \mu_1 \right)^2$ for the variance ($2^{nd}$ moment)?
user4933
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1 Answers1

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The $kth$ non central moment is

$E(X^k) $,

while the central one is defined as

$E[(X-E(X))^k] $.

Sample analogues are computed by replacing the expectations with averages, eg

$ \sum_i (x_i-\mu_1)^7/n $

Three Diag
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