CHARACTERIZATIONS OF THE EXPONENTIAL DISTRIBUTION BY RECORD VALUES

  • Chang, Se-Kyung (Department of Mathematics Education Cheongju University) ;
  • Lee, Min-Young (Department of Applied Mathematics Dankook University)
  • Received : 2006.11.01
  • Published : 2006.12.31

Abstract

This paper presents characterizations based on the identical distribution and the finite moments of the exponential distribution by record values. We prove that $X{\in}EXP({\sigma})$, ${\sigma}$>0, if and only if $X_{U(n+k)}-X_{U(n)}$ and $X_{U(n)}-X_{U(n-k)}$ for n > 1 and $k{\geq}1$ are identically distributed. Also, we show that $X{\in}EXP({\sigma})$, ${\sigma}$>0, if and only if $E(X_{U(n+k)}-X_{U(n)})=E(X_{U(n)}-X_{U(n-k)})$ for n>1 and $k{\geq}1$.

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