On characterization of multivariate stable distributions via random linear statistics

1995 ◽  
Vol 8 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Wei-Bin Zeng
Keyword(s):  
Stable Distributions ◽  
Linear Statistics

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

1976 ◽  
Vol 13 (2) ◽  
pp. 385-391 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Functional Equation ◽  
Weibull Distribution ◽  
Exponential Distribution ◽  
Stable Distribution ◽  
Stable Distributions ◽  
Cauchy Functional Equation ◽  
Linear Statistics

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.

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

1976 ◽  
Vol 13 (02) ◽  
pp. 385-391
Author(s):  
Y. H. Wang
Keyword(s):  
Functional Equation ◽  
Weibull Distribution ◽  
Exponential Distribution ◽  
Stable Distribution ◽  
Stable Distributions ◽  
Cauchy Functional Equation ◽  
Linear Statistics

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 allx,y≧ 0;(2) a characterization of the symmetricα-stable distribution by the equidistribution of linear statistics.

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