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A functional equation and its application to the characterization of the Weibull and stable distributions

Published online by Cambridge University Press:  14 July 2016

Y. H. Wang
Affiliation:
Concordia University, Montreal, Canada

Abstract

The Cauchy functional equation Φ(x + y) = Φ(x) + Φ(y) is generalized to the form , assuming Φ is left- or right- continuous. This result is used to obtain (1) a characterization of the Weibull distribution, in the spirit of the memoryless property of the exponential distribution, by , for all x, y ≧ 0;(2) a characterization of the symmetric α-stable distribution by the equidistribution of linear statistics.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1976 

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References

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