Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 4, 715--721

On Characteristic Properties of the Uniform Distribution

G. Arslan, Ba\c{s}kent University, Turkey
M. Ahsanullah, University of South Florida, USA
I.G. Bayramoglu (Bairamov), \.{I}zmir University of Economics, Turkey

SUMMARY. In this paper two characterizations of the uniform distribution using record values will be considered.  The first characterization is based on the relation $X_{U(m)}-X_{U(m-1)} \stackrel{d}{=} X_{L(m)}$, $m > 1$, where $X_{U(m)}$ and $X_{L(m)}$ denote the $m$-th upper and lower record values, respectively. The second characterization involves the second record range.

AMS (2000) subject classification. 62E10, 62G30.

Key words and phrases. Characterization, uniform distribution, Choquet-Deny Theorem, records, record range.

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