A test of the concavity of a distribution function with support contained in the unit interval may be based on a statistic constructed from the $L^p$-norm of the difference between an empirical distribution function and its least concave majorant. It is shown here that the uniform distribution is least favorable for such a test, in the sense that the limiting distribution of the statistic obtained under uniformity stochastically dominates the limiting distribution obtained under any other concave distribution function.
翻译:使用单位间隔内所含支持的分布函数的混凝度测试,可以基于以美元为基点,根据经验分布函数与其最小凝固主元值之间的差值计算出的统计数据。这里显示,统一分布最不利于这种测试,因为根据统一性得出的统计数据的有限分布在限制分配方面支配着在任何其他组合分布函数下获得的有限分布。