## The Annals of Probability

### Characterization of Subclasses of Class $L$ Probability Distributions

#### Abstract

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 $L$.

#### Article information

Source
Ann. Probab., Volume 6, Number 2 (1978), 279-293.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995573

Digital Object Identifier
doi:10.1214/aop/1176995573

Mathematical Reviews number (MathSciNet)
MR471022

Zentralblatt MATH identifier
0409.60017

JSTOR
Kumar, A.; Schreiber, B. M. Characterization of Subclasses of Class $L$ Probability Distributions. Ann. Probab. 6 (1978), no. 2, 279--293. doi:10.1214/aop/1176995573. https://projecteuclid.org/euclid.aop/1176995573