兩個逆高斯分配的平均值及尺度參數之廣義推論

Abstract

逆高斯分配在分析全為正數且右偏的數據時是一個很好的模型，因此在統計應用上很受重視。過去的研究中，在不假設干擾參數相等的情況下比較兩個母體的平均值及尺度參數的推論還需要我們繼續研究。因此在本論文中，我們利用廣義p值法對於一個及兩個逆高斯分配母體參數尋求精確的檢定方法，並提出一個在使用上比過去更為便利的方法，而這個方法是建立在廣義方法的觀念上，解決了在使用過去文獻中檢定兩個母體平均值的比例和計算信賴區間時會遇到的困難，也就是統計量中包含了干擾參數的問題，而且我們也得到了確切的解。藉由實際數據的分析，我們發現我們的方法跟過去的方法比較起來可以得到長度最短或是很接近最短的信賴區間長度。並且在模擬的研究中，我們可以看出我們的方法所得出的覆蓋率與型I誤差都很接近我們所設定的水準。

The IG distribution has gotten intensive attentions in statistical application fields by reason of it is an ideal candidate for modeling positive, right-skewed data. The classical procedures have difficulties in analysis non-homogeneous IG data. Hence, the exact inferences on making inferences for two IG means and scales deserve further research. In this thesis, we present a convenient approach based on the generalized p-value and generalized confidence methods to perform the hypothesis testing and confidence intervals for mean and scale of one IG population as well as the ratio of means and scales of two independent IG populations. Illustrative examples show that the confidence lengths obtained by the generalized methods are the smallest or close to the smallest length. Furthermore, the simulation studies show that our coverage probabilities and type I error are very close to the nominal levels.