### 摘要

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.

原文 | English |
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頁（從 - 到） | 1245-1264 |

頁數 | 20 |

期刊 | Taiwanese Journal of Mathematics |

卷 | 16 |

發行號 | 4 |

DOIs | |

出版狀態 | Published - 2012 一月 1 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

## 指紋 深入研究「A characterization of distributions by random summation」主題。共同形成了獨特的指紋。

## 引用此

Hu, C. Y., & Cheng, T. L. (2012). A characterization of distributions by random summation.

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