A simple characterization of Student's distributions and normal distributions

Document Type

Article

Publication Date

8-1-2011

Abstract

Let X1:3≤X2:3≤X3:3 be the order statistics of the independent and identically distributed random variables X1, X2, and X3. Using the regressional property E[(aX2:3-X1:3)2|X2:3=x]=E[(X3:3-aX2:3)2|X2:3=x], we characterize some distributions, including Student's tν distributions (ν>2) and normal distributions. © 2011.

Publication Title

Statistics and Probability Letters

First Page Number

903

Last Page Number

906

DOI

10.1016/j.spl.2011.03.037

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