In this post, we will derive the kurtosis of stand Gaussian distribution

is 3. We use the following equation to calculate the fourth central moment

The fourth central moment is

Therefore, the kurtosis is

For an application of Kurtosis analysis in saliency detection/in-focus segmentation, please refer to our paper and source code.

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Reycan I know how you get 3 for the last term? Is e^(-1/2)*(x^2) integrateable?