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題 名 | 多重掃瞄統計量之機率分配=Distribution of the Multiple Scan Statistic |
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作 者 | 林千代; 胡書銘; | 書刊名 | 中國統計學報 |
卷 期 | 34:3 1996.09[民85.09] |
頁 次 | 頁321-334 |
分類號 | 319.1 |
關鍵詞 | 間距; Stirling數; 符號計算; Spacings; Stirling numbers; Symbolic computation; |
語 文 | 中文(Chinese) |
中文摘要 | 多重掃瞄統計量 (Multiple Scan Statistic) 常被流行病學家用來作為檢定病情的隨機均勻性 (uniformity) 或群集性 (clustering) 的統計量。在本篇論文我們獲得多重掃瞄統計量k次動差的一般式。利用所得到的一般式及Huffer and Lin (1995) 所提出的演算法 (algorithm),我們介紹一套簡單而且精確的方法來計算多重掃瞄統計量的完全機率分配。三個以“動差法 (method of moments)” 為原則的逼近方法也於本論文中進行討論:第一個逼近法是牽涉一個簡單的二階段馬可夫鏈(Markov chain) 模式 (簡稱MC),而後兩個則是兩種擁有不同形式參數值的複合卜瓦松 (compound Poisson) 逼近法。經由模擬實驗研究,我們發現MC逼近法比其他二法表現較為精確。 |
英文摘要 | The multiple scan statistic is often used in epidemiological studies to test the null hypothesis of uniformity against a clustering alternative. In this article we derive a general expression for the kth moment of the multiple scan statistic. Utilizing these expressions and the algorithm proposed by Huffer and Lin (1995), we introduce a simple and accurate method to evaluate the distribution of the multiple scan statistic. This article also investigates the accuracy of three existing approximations for the distribution of the multiple scan statistic. Two basic types of “method of moments” approximations-one involves a simple Markov chain (MC) model, and others use to different compound Poisson approximations-are studied. A simulation study is presented to evaluate the accuracy of these approximations. Based on the numerical results, the MC approximation appears to be the most accurate one. |
本系統中英文摘要資訊取自各篇刊載內容。