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February, 1984 A Note on the Behavior of Sample Statistics when the Population Mean is Infinite
Jeesen Chen, Herman Rubin
Ann. Probab. 12(1): 256-261 (February, 1984). DOI: 10.1214/aop/1176993388

Abstract

Let $X_i \geq 0$ be i.i.d. random variables with $E(X_i) = \infty$. Then for suitable functions $\varphi$ we have $\overline{\varphi(X)}/\varphi(\bar{X}) \rightarrow 0$ a.s. We give some applications of this result.

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Jeesen Chen. Herman Rubin. "A Note on the Behavior of Sample Statistics when the Population Mean is Infinite." Ann. Probab. 12 (1) 256 - 261, February, 1984. https://doi.org/10.1214/aop/1176993388

Information

Published: February, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0551.60034
MathSciNet: MR723744
Digital Object Identifier: 10.1214/aop/1176993388

Subjects:
Primary: 60F99
Secondary: 62F99 , 62G99

Keywords: moments , nonexistence of moments , sums of random variables

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 1 • February, 1984
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