Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T20:51:09.892Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Ahlfors, L. V., Complex analysis. (McGraw-Hill, Second Edition, 1966).Google Scholar
2. Fréchet, M. and Shohat, J., A proof of the generalized second-limit theorem in the theory of probability. Trans. Amer. Math. Soc. 33 (1931) 533–543.Google Scholar
3. Loéve, M., Probability theory. (Van Nostrand, Second Edition, 1960).Google Scholar
4. Lukacs, E., Characteristic functions. (Charles Griffin and Co. Ltd.. 1960).Google Scholar
5. von Bahr, B., On the convergence of moments in the central limit theorem. Ann. Math. Statist. 36 (1965) 808–818.Google Scholar