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 |
|---|---|
| Pages (from-to) | 1245-1264 |
| Number of pages | 20 |
| Journal | Taiwanese Journal of Mathematics |
| Volume | 16 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2012 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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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 journal › Article
TY - JOUR
T1 - A characterization of distributions by random summation
AU - Hu, Chin Yuan
AU - Cheng, Tsung Lin
PY - 2012/1/1
Y1 - 2012/1/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=84864067496&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84864067496&partnerID=8YFLogxK
U2 - 10.11650/twjm/1500406734
DO - 10.11650/twjm/1500406734
M3 - Article
AN - SCOPUS:84864067496
VL - 16
SP - 1245
EP - 1264
JO - Taiwanese Journal of Mathematics
JF - Taiwanese Journal of Mathematics
SN - 1027-5487
IS - 4
ER -