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Application of a Weierstrass Theorem to the Convergence of Moments

Published online by Cambridge University Press:  20 November 2018

L.K. Chan  and
E.R. Mead
L.K. Chan
Affiliation:
University of Western Ontario
E.R. Mead
Affiliation:
University of Western Ontario
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In this note we apply a well-known theorem due to Weierstrass to show that under certain conditions convergence in distribution of a sequence of distribution functions implies the convergence of moments.

This note may be understood by an undergraduate student who has an introductory course of complex variables and a second course of statistics.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 1 , February 1969 , pp. 86 - 90
Copyright
Copyright © Canadian Mathematical Society 1969

References

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5. von Bahr, B., On the convergence of moments in the central limit theorem. Ann. Math. Statist. 36 (1965) 808–818.Google Scholar