在傳統的迴歸模型中，大多假設資料服從常態分配，然而當反應變數的範圍為正實數時，常態假設往往並不適用 。本文針對連續正實數資料，探討 Beta Prime 分配之迴歸模型與負二項分配之強韌概似函數，在估計上的表現與差異。 研究中利用強韌概似函數，分別計算強韌變異數估計量 、強韌華德檢定統計量與強韌概似比檢定統計量，並分析各檢定方法所對應之信賴區間與覆蓋機率。透過模擬研究與實例資料分析，我們發現強韌概似函數在不同資料分配條件下皆能提供準確的估計，即使在真實分配未知的情況下 ，仍能有良好估計結果 。相較之下，當資料偏離 Beta Prime假設時，即使保持相同的迴歸架構，Beta Prime 迴歸模型的估計準確度仍大幅下降，且隨著變異數增大表現更不理想。整體結果顯示，強韌概似函數在理論與實務層面皆展現出高度穩健性與彈性。;Traditional regression models often assume that the data follow a normal distribution. However, when the response variable is restricted to the positive real line, this assumption becomes inappropriate. This study focuses on continuous positive data and compares the estimation performance of the Beta Prime regression model and the robust likelihood function based on the negative binomial distribution. In our analysis, we use the robust likelihood approach to compute robust variance estimators, robust Wald test statistics, and robust likelihood ratio test statistics. We also examine the corresponding confidence intervals and coverage probabilities derived from these tests. Through simulation studies and real data applications, we find that the robust likelihood function provides accurate and stable estimates under various data-generating distributions.Even when the true distribution is unknown, the method still performs reliably. In contrast, the Beta Prime regression model is highly sensitive to deviations from its distributional assumption. When the data do not follow a Beta Prime distribution, the estimation accuracy of the model declines substantially, particularly as the variance increases. Overall, the results demonstrate that the robust likelihood function exhibits high levels of theoretical soundness and practical flexibility, making it a suitable inference tool for positive continuous data.
