離散分布的預測區間

Abstract

預測區間估計是一個重要工具，可用來預測在醫學、藥物及工業的疾病個 數和生產線的故障率。目前文獻上的預測區間估計方法在離散分佈的研究 上跟連續分佈的研究相比，較欠缺令人滿意的結果。尤其在二項分佈時， 當成功比率靠近邊界點時，傳統的方法較難得到很好的結果。因此，在此 研究中，我們擬先對二項分布提出一個改進的預測區間。從覆蓋率的準則， 我們預期新的預測區間能比傳統的預測區間有較好的覆蓋率。除了以覆蓋 率當準則外，我們會另外用Kullback-Leibler 距離的準則來跟傳統的預測 區間做比較。除了二項分布外預計將此結果推廣一般的離散分佈上並實際 的工業及醫學例子上，來驗證此方法的可信度。

A prediction interval is an important tool in industry or medical applications to predict the number of shutdown occurred of a producing process or the number of disease occurred in a population. The performances of the existing prediction intervals are unsatisfactory when the true proportion of defective number is near the boundaries. However, in real applications, the true proportion could be very small. Therefore, in this study, we will propose improved prediction intervals with better coverage probability than the existing methods. Their predictive distributions are compared in terms of Kullback-Leibler distance criterion. The comparison of the intervals are illustrated by industry and medical examples.