在雙變數對數常態模式下比較兩組母體期望值的比值

Abstract

雙變數對數常態分布普遍被用在許多應用上，Bebu and Mathew (2008) 用廣義信賴區間方法去尋找探討雙變數對數常態期望值比值的信賴區間，不論其樣本數大小為何。在兩組的配對研究中，比較兩組雙變數對數常態分布的期望值比值一直是感興趣且重要的研究重點。我們推廣Bebu and Mathew (2008) 的方法去比較在兩組雙變數對數常態分布模式下的兩組期望值比值，特別要注意的是，本項研究的目的是建構雙變數對數常態期望值之比值的信賴區間，此信賴區間是藉由導出兩組雙變數對數常態分布之兩組期望值比值的樞紐統計量的抽樣步驟而得。在模擬研究中，覆蓋率和檢定力均被計算且研究被推薦的方法表現如何，而模擬結果指出覆蓋率和檢定力都有好的表現，就算樣本數沒有很大。

The bivariate log-normal distributions are commonly used in many applications. Bebu and Mathew (2008) use the generalized confidence interval approach to develop a confidence interval for the ratio of the bivariate log-normal means regardless of the sample size. It is often of interest to comparing the mean ratios of two bivariate log-normal distributions in two-arm paired studies. We then extend Bebu and Mathew (2008) approach for comparing two mean ratios under the two bivariate log-normal distributions. Specifically, this study is to construct a confidence interval for the ratio of the bivariate log-normal means by deriving the sampling procedures for pivotal statistics of two mean ratios in two bivariate log-normal distributions. In the simulation study, the coverage rate and the power are calculated to study the performance of the proposed approach. The simulation results indicate that the coverage rate and the power perform well even when sample size is not large.