頁籤選單縮合
題名 | A Characterization of Distributions by Random Summation= |
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作者 | 胡金源; 鄭宗琳; Hu, Chin-yuan; Cheng, Tsung-lin; |
期刊 | Taiwanese Journal of Mathematics |
出版日期 | 20120800 |
卷期 | 16:4 2012.08[民101.08] |
頁次 | 頁1245-1264 |
分類號 | 314.5 |
語文 | eng |
關鍵詞 | Characteristic function; Random summation; |
英文摘要 | 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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