Re: Existence of an expectation
- From: hrubin@xxxxxxxxxxxxxxx (Herman Rubin)
- Date: 12 Oct 2005 15:10:05 -0500
In article <2390777.1129124224936.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
anz3 <ants33b@xxxxxxxxx> wrote:
>Let X be a random variable with X>0 a.s. and E(ln(X)) < \infty . Is it correct
>that in general it is not possible to conclude that there exists \epsilon > 0
>such that E(X^\delta) < \infty for 0 < \delta < epsilon or E(X^\delta) < \infty
>for 0 > \delta > - \epsilon? Thank you very much in advance for your answers.
If one lets Y = ln(X), the problem is equivalent to
E(|Y|) finite, and one wants to know if E(exp(t*Y)
is finite for any positive or negative t. We know
lots of counterexamples to this, even if E(|Y|^k)
is finite for all k.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
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- Existence of an expectation
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