ABSTRACT In this paper, a pivot function which is in terms of the sample and the underlying population distribution is introduced. It is assumed that the population distribution is continuous and strictly increasing on its support. Then, the martingale central limit theorem is applied to prove that limiting distribution of the pivot function is the standard normal. Interestingly, this result provides a unified procedure that can be applied for the goodness of fit, and for the purpose of parametric and nonparametric inferences, for the populations having distribution functions that are continuous and strictly increasing on their supports. The method is fairly simple and can be easily applied.

中文翻译：

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枢轴函数及其极限分布：在拟合优度和检验假设中的应用

摘要 在本文中，引入了一个关于样本和潜在人口分布的枢轴函数。假设人口分布是连续的，并且在其支持下严格增加。然后，应用鞅中心极限定理证明枢轴函数的极限分布是标准正态分布。有趣的是，该结果提供了一个统一的程序，可用于拟合优度以及参数和非参数推理的目的，用于具有连续且在其支持上严格递增的分布函数的总体。该方法相当简单，易于应用。