Characterizing Exponential Distributions via Conditional Independence

Abstract

Let Y1,...,Yn be n mutually independent, nonnegative random variables such that for each i=1,...,n,Yi has an absolutely continuous distribution function function F(x;0i) = F(0xi), where 0i>O, and F(.) has support O,oo). We show that given Yi - Yi+1>O for all i+1,...,n-1, the necessary and sufficient condition for the random variables Y1 - Y2,...,Yn-1-Yn and Yn to be conditionally mutually independent is that for each i+1,...,n,Yi has an exponential distribution. Characterization; Exponential distribution; Conditional independence.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1990
Accession Number
ADA219255

Entities

People

  • Tachen Liang

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  • Purdue University

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Fields of Study

  • Mathematics

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  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.