## Taiwanese Journal of Mathematics

### A CHARACTERIZATION OF DISTRIBUTIONS BY RANDOM SUMMATION

#### Abstract

In this paper, we consider a problem of characterizing distribution through the constructive property of random sum $p S_N$, where $0 \lt p \lt 1$ and $N \geq 0$ is an integer-valued random variable. This problem will be solved under someregular conditions. We extend the characterization of exponential distribution to ageneral case. For example, the gamma distribution, the positive Linnik distributionand the scale mixture of stable distribution are characterized. Two new results inthe vein are obtained. Finally, the problem of characterizing distribution by theproperty of the first order statistics is also investigated.

#### Article information

Source
Taiwanese J. Math., Volume 16, Number 4 (2012), 1245-1264.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406734

Digital Object Identifier
doi:10.11650/twjm/1500406734

Mathematical Reviews number (MathSciNet)
MR2951138

Zentralblatt MATH identifier
1259.62004

Subjects
Primary: 621E0

#### Citation

Hu, Chin-Yuan; Cheng, Tsung-Lin. A CHARACTERIZATION OF DISTRIBUTIONS BY RANDOM SUMMATION. Taiwanese J. Math. 16 (2012), no. 4, 1245--1264. doi:10.11650/twjm/1500406734. https://projecteuclid.org/euclid.twjm/1500406734

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