犯两类错误概率相等的检验函数

On The Test In Which Two Frroneous Probability Are Equal

设有总体X具有概率密度或概率分布列f(x,θ),θ未知,θ∈(?)={θ_0,θ_1},要检验假设(?),样本X_1,X_2、…、X_n 本文为克服最优势检验中原假设与备择假设地位不对称的矛盾,提出了一种检验法则:此检验函数具有与最优势检验形式相同的检验函数,且犯第一、第二两类错误的概率相等。本文证明了这样的检验验函数是存在的,并且举例以说明之。

Assume that Ⅹ is a random variable whose density function f(x, θ) is iudexed by the parameter θ, and θ is unknown. Assume the X_1, X_2, …, X_n, is a random sample of Ⅹ. We desire to test H_0: θ=θ_1 where θ_0 and θ_1 are two specific valuse for θ.In this paper, we give a testing criterion in which the form of testing function is same as the most powerful testing function, but the probability of type Ⅰ error is equal the probability of type Ⅱ error.We prove the existence of such tetting function and give some examples also.