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A note on moment generating functions

Author

Listed:
  • Mukherjea, A.
  • Rao, M.
  • Suen, S.

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].

Suggested Citation

  • Mukherjea, A. & Rao, M. & Suen, S., 2006. "A note on moment generating functions," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1185-1189, June.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:11:p:1185-1189
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    Cited by:

    1. Ushakov, N.G. & Ushakov, V.G., 2011. "On convergence of moment generating functions," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 502-505, April.
    2. Fung, Thomas & Seneta, Eugene, 2010. "Tail dependence for two skew t distributions," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 784-791, May.
    3. Guy Katriel, 2014. "Directed Random Market: the equilibrium distribution," Papers 1404.4068, arXiv.org.

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