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I am beginning to appreciate how important Moment Generating Functions (MGFs) are regarding various common probability distributions and the ways their expectations/variances are calculated.

My open-ended question is: What is the history of MGFs? Who was first to develop them/introduce notation/generalize properties of MGFs?

Please don't close this question or put it on hold because it is primarily opinion-based; I just haven't been able to find any information about the history of MGFs and I'm very curious about their origin/development.

Xoque55
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    I had a look in the index of Stigler and there was nothing obvious. Would be a good one for the http://meta.math.stackexchange.com/questions/12773/area-51-proposal-history-of-mathematics-and-science if it gets off the ground. – TooTone Mar 02 '14 at 00:30

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This is an interesting question! By searching on JSTOR, the oldest paper I found where the term moment generating function is used (in some statistical context) is the following paper: Rider, Paul R. “A Survey of the Theory of Small Samples.” Annals of Mathematics, vol. 31, no. 4, 1930, pp. 577–628. Second Series, www.jstor.org/stable/1968155. which actually looks somewhat modern! As the moment generating function is related to the Laplace transform, some answers here: What kind of book would show where the inspiration for the Laplace transform came from? might be helpful

(I will come back to this question continuing the search for early papers)

kjetil b halvorsen
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