A CHARACTERIZATION BASED ON THE ABSOLUTE DIFFERENCE OF TWO I. I. D. RANDOM VARIABLES

Abstract

Let X be a nonnegative random variable with X sub 1 and X sub 2 as its two independent copies. The problem considered here is to characterize all the nonnegative distributions with the property that the distribution of the absolute difference /(X sub 1)-(X sub 2)/ is the same as that of X. It is shown that in general such a distribution has to be either purely discrete, or absolute continuous or singular and that it cannot be their mixture.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1970
Accession Number
AD0700291

Entities

People

  • Herman Rubin
  • Prem S. Puri

Organizations

  • Purdue University

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  • Biomedical

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  • Discrete Distribution
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Fields of Study

  • Mathematics

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  • Fluid Dynamics.
  • Linear Algebra