Testing Homogeneity of Uniform Scale Distributions Against Two-Sided and One-Sided Alternatives
研究了检验多个均匀分布尺度参数是否相等的统计方法，包括双侧和单侧备择假设，证明了似然比检验的无偏性，并给出了精确和渐近分布，结果也适用于指数分布位置参数的同质性检验，对可靠性分析有重要应用。
Abstract Consider the model where Xij, i = 1, 2, …, k; j = 1, …, n i are independent uniform random variables with scale parameter θ i > 0. Test H 0: θl = ··· = θ k versus H 2: not H 0. Also consider the alternative H 1: θl ≤ ··· ≤ θ k . For H 0 versus H 2 and n i = n, we obtain a complete class of constant-size permutation invariant tests and show that each test in the class is unbiased. The likelihood ratio test and others are in this class. For H 0 versus H 1 we obtain a complete class of constant-size tests based on a set of variables that is a transformation of the sufficient statistics. Again we show that each test in the class is unbiased. The likelihood ratio test is in this class. We derive the exact and asymptotic distribution of the likelihood ratio test. All results also hold for testing homogeneity of location parameters of exponential distributions. This latter case is of considerable practice importance in reliability.