Minimal-Moment Generating Functions
A characteristic function determines, through an integration formula, the probability distribution
of the associated random variable
so there is a one to one relationship between characteristic functions and probability distributions.
A remarkable result called the continuity theorem says that if the
characteristic functions of a sequence of random variables converge to a function continuous at 0,
then that function must be a
characteristic function and furthermore, the sequence of
associated random variables converges weakly to its random variable.
By the time of W. Hoeffding in the early 1950's it was known that in analogy with the
usual moments (expectations of powers) of a random variable,
the maximal moments (expectations of the maxima of independent collections of random variables)
determined the probability distribution. Minimal moments are analogous. Here
a minimal moment
generating function is defined and shown to have properties analogous to those of the characteristic
function, See also the published version in the journal Extremes.
published by Springer.