Has anyone ever seen a proof of the following. For an iid sample where
X_{(N)} is the Nth order statistic that the \frac{\partial
E[X_{(N)}]}{\partial \sigma^2} \geq 0. That is, as the variance of the
parent distribution increases the expected value of the order statistic for
a given and finite N also increases. Similarly, the expected value of the
minimum order statistic would decline as the variance of the parent
distribution increases.
In advance, thank-you for any assistance or direction.
Alan
Alan Ker
Department of Agricultural and Resource Economics,
University of Arizona,
Tucson, Az 85721-0023
ph (520) 621-6265
fax (520) 621-6250
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