Explicit Expression of P Value and Its Probability Distribution Properties
张洪1
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作者信息
1. 中国科学技术大学 管理学院,合肥 230026
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摘要
针对几个常见的假设检验问题,首先给出检验 P 值的显式表达式,然后推导出 P 值作为一个随机变量的概率分布,接着证明P值在满足如下三个条件下服从均匀分布:真实参数为最接近对立假设的原假设参数值、检验统计量的相应零分布被正确指定、该零分布的分布函数可逆.
Abstract
For several common hypothesis testing problems,we first provide an explicit expression for the P-value of hypothesis testing,then derive the probability distribution of the P-value as a random variable.We prove that the P-value follows a uniform distribution under the following three conditions:the true parameter is the null hypothesis parameter value closest to the alternative hypothesis,the corresponding null distribution of the test statistic is correctly specified,and the distribution function of the null distribution is invertible.
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