利用高階概似方法對多個逆高斯分配的共同平均數建構信賴區間

Abstract

這篇文章裡我們討論了關於多個異質的逆高斯分配的共同平均數信賴區間的估計。我們所利用的方法是以概似函數為基礎的高階近似方法，並且我們利用模擬的方法去跟signed log-likelihood ratio及 simple t-test 兩種方法比較所建構出的信賴區間的覆蓋機率和平均寬度以及所對應檢定的型I錯誤來檢視我們所利用方法的優劣。結果顯示我們所提出的方法即使在小樣本的情況下表現的很好，而且相對來說比前述的兩種方法可以提供更穩定、正確的結果。最後我們提供了兩個例子作為說明。

An interval estimation method for the common mean of several non-homogeneous inverse Gaussian (IG) populations is discussed. The proposed method is based on a higher order likelihood-based asymptotic procedure. The merits of the proposed method are numerically compared with the signed log-likelihood ratio statistic and the simple t-test method with respect to their expected lengths, coverage probabilities and type I errors. Numerical studies show that the coverage probabilities of the proposed method are very accurate even for very small samples. The methods are also applied to two examples.