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 languageEnglish
Pages (from-to)1245-1264
Number of pages20
JournalTaiwanese Journal of Mathematics
Volume16
Issue number4
DOIs
Publication statusPublished - 2012 Jan 1

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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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A characterization of distributions by random summation. / Hu, Chin Yuan; Cheng, Tsung Lin.

In: Taiwanese Journal of Mathematics, Vol. 16, No. 4, 01.01.2012, p. 1245-1264.

Research output: Contribution to journalArticle

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