# A characterization of distributions by random summation

Chin Yuan Hu, Tsung Lin Cheng

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

In this paper, we consider a problem of characterizing distribution through the constructive property of random sum pSN, where 0 < p < 1 and N ≥ 0 is an integer-valued random variable. This problem will be solved under some regular conditions. We extend the characterization of exponential distribution to a general case. For example, the gamma distribution, the positive Linnik distribution and the scale mixture of stable distribution are characterized. Two new results in the vein are obtained. Finally, the problem of characterizing distribution by the property of the first order statistics is also investigated.

Original language English 1245-1264 20 Taiwanese Journal of Mathematics 16 4 https://doi.org/10.11650/twjm/1500406734 Published - 2012 Jan 1

### Fingerprint

Characterization of Distributions
Summation
Random Sums
Scale Mixture
Stable Distribution
Veins
Gamma distribution
Exponential distribution
Order Statistics
Random variable
First-order
Integer

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

### Cite this

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abstract = "In this paper, we consider a problem of characterizing distribution through the constructive property of random sum pSN, where 0 < p < 1 and N ≥ 0 is an integer-valued random variable. This problem will be solved under some regular conditions. We extend the characterization of exponential distribution to a general case. For example, the gamma distribution, the positive Linnik distribution and the scale mixture of stable distribution are characterized. Two new results in the vein are obtained. Finally, the problem of characterizing distribution by the property of the first order statistics is also investigated.",
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In: Taiwanese Journal of Mathematics, Vol. 16, No. 4, 01.01.2012, p. 1245-1264.

Research output: Contribution to journalArticle

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AU - Cheng, Tsung Lin

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AB - In this paper, we consider a problem of characterizing distribution through the constructive property of random sum pSN, where 0 < p < 1 and N ≥ 0 is an integer-valued random variable. This problem will be solved under some regular conditions. We extend the characterization of exponential distribution to a general case. For example, the gamma distribution, the positive Linnik distribution and the scale mixture of stable distribution are characterized. Two new results in the vein are obtained. Finally, the problem of characterizing distribution by the property of the first order statistics is also investigated.

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