A functional equation and its application to the characterization of the Weibull and stable distributions
- 1 June 1976
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (2) , 385-391
- https://doi.org/10.2307/3212846
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.Keywords
This publication has 6 references indexed in Scilit:
- A Note on the "Lack of Memory" Property of the Exponential DistributionThe Annals of Probability, 1975
- Characterizations of the normal distribution by suitable transformationsJournal of Applied Probability, 1973
- Characterization of distributions by the identical distribution of linear formsJournal of Applied Probability, 1966
- On a linear form whose distribution is identical with that of a monomialPacific Journal of Mathematics, 1965
- CHARACTERIZATION OF POPULATIONS BY PROPERTIES OF SUITABLE STATISTICSPublished by University of California Press ,1956
- Sur l'équation fonctionnelle f(x+y)=f(x)+f(y)Fundamenta Mathematicae, 1920