NOTE ON THE MOMENT GENERATING FUNCTION OF THE MULTIVARIATE NORMAL DISTRIBUTION

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Abstract

We present a streamlined proof of a formula for the derivatives of the moment generating function of the multivariate normal distribution. We formulate it in terms of the summation of the contractions by pairings, which encodes a combinatorial computation procedure. We give two applications. First, we provide a simple proof of Isserlis’ theorem and derive a formula for the moments of the multivariate normal distribution.Second, we calculate the moments of the product of a finite number of correlated normally and lognormally distributed random variables.

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Hirose, K. (2024). NOTE ON THE MOMENT GENERATING FUNCTION OF THE MULTIVARIATE NORMAL DISTRIBUTION. Miskolc Mathematical Notes, 25(1), 287–300. https://doi.org/10.18514/MMN.2024.4255

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