Definition of moment generating function in English:

moment generating function

noun

Statistics
  • A function from which each of the moments of a given random variable can be derived, the kth moment being equal to the kth derivative of the function, evaluated at zero; (formerly also) †a function from which the product moments of a given set of data can be similarly derived (obsolete).

Origin

1930s; earliest use found in Annals of Mathematical Statistics.