A note on moment generating functions

A. Mukherjea, M. Rao and S. Suen

Statistics & Probability Letters, 2006, vol. 76, issue 11, 1185-1189

Abstract: In this note, we show that if a sequence of moment generating functions Mn(t) converges pointwise to a moment generating function M(t) for all t in some open interval of R, not necessarily containing the origin, then the distribution functions Fn (corresponding to Mn) converge weakly to the distribution function F (corresponding to M). The proof uses the basic classical result of Curtiss [1942. A note on the theory of moment generating functions. Ann. Math. Statist. 13 (4), 430-433].

Date: 2006
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