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April, 1978 Characterization of Subclasses of Class $L$ Probability Distributions
A. Kumar, B. M. Schreiber
Ann. Probab. 6(2): 279-293 (April, 1978). DOI: 10.1214/aop/1176995573


The subclasses of class $L$ probability distributions recently studied by K. Urbanik are characterized by requiring that certain functions be convex and have derivatives of some fixed order. The extreme points of certain compact convex sets of probability measures are determined, and this information is then used to obtain a representation of the characteristic functions of the probability distributions in those classes, in the same manner as Urbanik has proceeded for the class $L$.


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A. Kumar. B. M. Schreiber. "Characterization of Subclasses of Class $L$ Probability Distributions." Ann. Probab. 6 (2) 279 - 293, April, 1978.


Published: April, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0409.60017
MathSciNet: MR471022
Digital Object Identifier: 10.1214/aop/1176995573

Primary: 60B15
Secondary: 28A50 , 60E05 , 60F05 , 60G50

Keywords: Characteristic function , completely monotonic function , convex function , extreme points , infinitely divisible distribution , Levy-Khincthine representation

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 2 • April, 1978
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