In the present paper, we develop a new goodness-of-fit test for the Birnbaum- Saunders distribution based on the probability plot. We utilize the sample correlation coefficient from the Birnbaum-Saunders probability plot as a measure of goodness of fit. Unfortunately, it is impossible or extremely difficult to obtain an explicit distribution of this sample correlation coefficient. To address this challenge, we employ extensive Monte Carlo simulations to obtain the empirical distribution of the sample correlation coefficient from the Birnbaum-Saunders probability plot. This empirical distribution allows us to determine the critical values alongside their corresponding significance levels, thus facilitating the computation of the p-value when the sample correlation coefficient is obtained. Finally, two real-data examples are provided for illustrative purposes.

翻译：本文提出了一种基于概率图的新型Birnbaum-Saunders分布拟合优度检验方法。我们利用Birnbaum-Saunders概率图中的样本相关系数作为拟合优度的度量。然而，该样本相关系数的显式分布难以或无法获得。为了解决这一难题，我们采用大规模蒙特卡洛模拟来获取Birnbaum-Saunders概率图样本相关系数的经验分布。该经验分布使我们能够确定临界值及其对应的显著性水平，从而在获得样本相关系数后可计算p值。最后，通过两个实际数据示例进行说明。