### Abstract

In this paper, we consider a problem of characterizing distribution through the constructive property of random sum _{p}S_{N}, 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 |
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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)

### Cite this

*Taiwanese Journal of Mathematics*,

*16*(4), 1245-1264. https://doi.org/10.11650/twjm/1500406734

}

*Taiwanese Journal of Mathematics*, vol. 16, no. 4, pp. 1245-1264. https://doi.org/10.11650/twjm/1500406734

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

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 -