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When, by whom and in which paper where moments of a random variable used first in probability theory?

Question moved to : https://hsm.stackexchange.com/questions/7343/who-introduced-moments-of-a-random-variable-first

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  • $\begingroup$ I agree "too broad" is not a good close reason. Maybe "not research mathematics" is OK as a close reason. On the other hand, citing a non-closed post from 5 years ago does not show what today's standards for closing are. $\endgroup$ – GEdgar May 9 '18 at 11:47
  • $\begingroup$ This feels like good scholarship to me $\endgroup$ – Julien__ May 9 '18 at 11:51
  • $\begingroup$ Personally, I did not vote to close. But in fact this question fits better at "History of Science and Mathematics" hsm.stackexchange.com $\endgroup$ – GEdgar May 9 '18 at 11:52
  • $\begingroup$ This sites deals with mathematical problems, and more specifically reasoning steps where the asker is stuck. Little to do with the history of Mathematics, hence off-topic. I just voted to close the question you linked to. $\endgroup$ – Yves Daoust May 9 '18 at 12:10
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From MathWords

Moment was taken into Statistics from Mechanics by Karl Pearson when he treated the frequency-curve (or observation curve) as the sheet enclosed by the curve and the horizontal axis. See his "Asymmetrical Frequency Curves," Nature October 26th 1893: "Now the centre of gravity of the observation curve is found at once, also its area and its first four moments by easy calculation." [OED].

 

The phrase method of moments was used in a statistics sense in the first of Karl Pearson’s "Contributions to the Mathematical Theory of Evolution," (Philosophical Transactions of the Royal Society A, 185, (1894), p. 75.). Pearson used the method to estimate the parameters of a mixture of normal distributions. For several years Pearson used the method on different problems but the name only gained general currency with the publication of his 1902 Biometrika paper "On the systematic fitting of curves to observations and measurements" (David 1995). In "On the Mathematical Foundations of Theoretical Statistics" (Phil. Trans. R. Soc. 1922), Fisher criticized the method for being inefficient compared to his own maximum likelihood method (Hald pp. 650 and 719).

 

Moment generating function. R. A. Fisher seems to have brought this term into English in his "Moments and Product Moments of Sampling Distributions.," Proceedings of the London Mathematical Society, Series 2, 30, (1929), p. 238. He probably took the term from V. Romanovsky "Sur Certaines Éspérances Mathématiques et sur l'Erreur Moyenenne du Coefficient de Corrélation, Comptes Rendus, 180, (1925), 1897-1899. Romanovsky refers to "la function génératrice des moments" (p. 1898).

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