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Formulae for absolute moments

Published online by Cambridge University Press:  09 April 2009

B. M. Brown
B. M. Brown
Affiliation:
La Trobe University
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The purpose of this note is to derive an alternative expression to that given in Lemma 1 below (due to Hsu, and to von Bahr) for the absolute moments of a random variable, in terms of the characteristic function.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 104 - 106
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Brown, B. M., ‘Characteristic functions, moments, and the central limit theorem’, Ann. Math. Statist. 41 (1970), 658–664.CrossRefGoogle Scholar
[2]Hsu, P. L., ‘Absolute moments and characteristic functions’, J. Chinese Math. Soc., 1 (1951) 259–280.Google Scholar
[3]Loeve, M., Probability theory, (2nd ed.) (van Nostrand, Princeton, 1960).Google Scholar
[4]Lukacs, E., Characteristic functions (Griffin, London, 1960).Google Scholar
[5]Pitman, E. J. G., ‘Some theorems on characteristic functions of probability distributions’, Proc. IVth Berk. Symp., (1960), 393–402.Google Scholar
[6]von Bahr, Bengt, ‘On the convergence of moments in the central limit theorem’, Ann. Math. Statist. 36 (1965), 808–818.CrossRefGoogle Scholar