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Characterization of certain populations by independence of order statistics

Published online by Cambridge University Press:  14 July 2016

János Galambos
János Galambos*
Affiliation:
Temple University, Philadelphia
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Abstract

A method, making use of characteristic functions, is presented to prove theorems on characterization of distributions by independence of order statistics. Since exact independence in practice is rarely achieved, much attention is being given in the literature to theorems on determining the distributions for which certain statistics are ‘almost’ independent. The technique of this new line of investigation is strongly dependent on the fact that for the case of exact independence there is a solution in terms of characteristic functions. The present work was guided by this fact. In addition to the new method, Theorem 2 appears to be new.

Keywords

CHARACTERIZATIONPOPULATIONINDEPENDENCEORDER STATISTICSCHARACTERISTIC FUNCTIONSABSOLUTELY CONTINUOUSEXPECTATIONDENSITY FUNCTIONBOREL MEASURABLE FUNCTIONFISZ'S THEOREM; LINEAR TRANSFORMATION

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 224 - 230
Copyright
Copyright © Applied Probability Trust 1972 

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References

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