Abstract We introduce a family of weighted omega-square statistics. We show that they provide a family of locally asymptotically optimal goodness-of-fit tests, in the sense of Bahadur, for the location problem associated with (type iv ) generalized logistic distributions. Our paper extends and unifies some results already known for the classical Cramer–von Mises and Anderson–Darling statistics which are optimal with respect to the hyperbolic secant and the logistic distributions.

中文翻译：

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广义逻辑分布位置族的具有巴哈杜尔局部最优性的新欧米茄平方型统计族

摘要 我们介绍了一系列加权欧米茄平方统计量。我们表明，在 Bahadur 的意义上，它们提供了一系列局部渐近最优拟合优度检验，用于与（类型 iv）广义逻辑分布相关的位置问题。我们的论文扩展并统一了一些已知的经典 Cramer-von Mises 和 Anderson-Darling 统计结果，这些结果对于双曲正割和逻辑分布是最优的。