本文提出利用強韌概似函數 (robust likelihood function) 方法比較多個非負隨機變數。此強韌檢定法是將多個獨立的伽瑪概似函數強韌化，得到強韌華德檢定統計量、強韌分數檢定統計量及強韌概似比檢定統計量，亦利用強韌檢定法建立共同平均數之信賴區間。利用模擬與實例分析，先比較強韌檢定法、Krishnamoorthy and Oral (2015) 提出的標準化概似比檢定統計量(standardized likelihood ratio test) 和 Bebu and Methew (2007) 利用廣義樞紐量(generalized pivot statistic) 建構之廣義信賴區間 (generalized confidence interval)，再比較利用強韌檢定法建立共同平均數之信賴區間和 Krishnamoorthy and Oral (2015) 改良 Zou et al. (2009) 提出的 MOVER 近似信賴區間方法建立之共同平均數信賴區間。;In this thesis, we propose a robust likelihood function method to analyze several nonnegative random variables. The robustness test method is not only for robustizing several independent gamma likelihood function to obtain robust Wald-type test statistic, robust score test statistic, and robust likelihood ratio test statistic, but also for constructing the confidence interval of common mean. By using both simulation and real data analysis, we can demonstrate the merit of our technique of robustness. At first, we compare the differences among robustness test method, the standardized likelihood ratio test proposed by Krishnamoorthy and Oral (2015), and the generalized confidence interval constructed by Bebu and Mathew (2007) which used the generalized pivot statistic. Additionally, we also compare the differences between the common mean confidence interval established by the MOVER approximate confidence interval method proposed by Krishnamoorthy and Oral (2015) modified Zou et al. (2009).
