两个Weibull分布尺度参数比的推断

Inference for the Ratio of Scale Parameters of Two Weibull Distributions

本文研究两个Weibull分布尺度参数比的推断.利用广义枢轴量和广义检验变量分别给出尺度参数比的广义置信区间和假设检验.证明了在形状参数相等时由广义枢轴量确定的尺度参数比的100(1-α)%广义置信区间的覆盖概率为1-α(0<α<1)由广义p-值确定的固定水平检验具有真实水平.讨论了形状参数不等时尺度参数比的推断,给出频率性质,通过与前人的结果模拟比较得出本文的方法能更好地解决尺度参数比的推断问题.最后研究两个Weibull分布形状参数比的假设检验,证明由广义p-值确定的固定水平检验具有真实水平.

In this article,inferences for the ratio of scale parameters of two Weibull distribution are studied.We propose the generalized confidence intervals and hypothesis testings for the ratio of scale parameters by generalized pivotal quantities and generalized test variables. When shape parameters are equal,the studies show that the covered probability of 100（1-α）%generalized confidence interval for the ratio of scale parameters is 1-α,and the Type-Ⅰerror rates is nominal significance levelα.When shape parameters are unequal, we also study frequency properties of inference,and the numerical studies show that the proposed generalized confidence and generalized p-values inferential proceduers are satisfactory. At last,hypothesis testings for the ratio of shape parameters are studied,we prove that the Type-Ⅰerror rates are nominal significance levelα.