Taiwanese Journal of Mathematics


Chin-Yuan Hu and Tsung-Lin Cheng

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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.

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

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 621E0

characteristic function random summation


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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