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| 題 名 | 連續成功次數的極限分布=A Note on the Sum of the Lengths of Maximal Success Runs |
|---|---|
| 作 者 | 趙民德; | 書刊名 | 中國統計學報 |
| 卷 期 | 35:2 1997.06[民86.06] |
| 頁 次 | 頁119-124 |
| 分類號 | 319.16 |
| 關鍵詞 | Poisson收斂; 常態收斂; 平穩過程; Poisson convergence; Normal convergence; Stationary process; |
| 語 文 | 中文(Chinese) |
| 中文摘要 | 周元燊(1992)曾用極簡潔的方法,討論了在一序列伯努利(Bernoulli)試驗中,自 j 次試驗算起的連續成功數 Nj 之和 Tn= Σ Nj 的 Poisson 極限定理, 並說明了在 p → 0, np →∞時,極限分布應為常態,但證明可能不容易簡潔。我們使用與周氏差不多一樣簡 潔的方法,證明了在且只有在 np →∞,np �纂� 0 時,他的猜測才是對的。 |
| 英文摘要 | Using a very elegant method, Chow (1992) discussed the limiting theorems on the sum of the maximal lengths of success runs defined via a Bernoulli process. He mentioned that when p → 0, np →∞, the proper limiting distribution is still normal, but indicated that the proof may not be simple. We employ a technique, about as simple as Chow's and show that Chow's conjecture is true if and only if np →∞, np �纂� 0. |
本系統中英文摘要資訊取自各篇刊載內容。