Annals of Probability

A Note on the Behavior of Sample Statistics when the Population Mean is Infinite

Jeesen Chen and Herman Rubin

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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.

Article information

Source
Ann. Probab., Volume 12, Number 1 (1984), 256-261.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993388

Digital Object Identifier
doi:10.1214/aop/1176993388

Mathematical Reviews number (MathSciNet)
MR723744

Zentralblatt MATH identifier
0551.60034

JSTOR
links.jstor.org

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 62G99: None of the above, but in this section 62F99: None of the above, but in this section

Keywords
Sums of random variables nonexistence of moments moments

Citation

Chen, Jeesen; Rubin, Herman. A Note on the Behavior of Sample Statistics when the Population Mean is Infinite. Ann. Probab. 12 (1984), no. 1, 256--261. doi:10.1214/aop/1176993388. https://projecteuclid.org/euclid.aop/1176993388


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