双参数指数分布检验问题中样本容量的确定  

The Determination of Sample Size in Two-Parameter Exponential Distribution

作　　者：黄圣杰 HUANG Sheng-jie(College of Mathematics and Statistics,Guangxi Normal University Guilin 541004,China)

机构地区：[1]广西师范大学数学与统计学院

出　　处：《广西民族大学学报（自然科学版）》2019年第3期62-64,68,共4页Journal of Guangxi Minzu University ：Natural Science Edition

摘　　要：在双参数指数分布的假设检验中,当样本容量确定时,两类错误存在"此消彼长"的关系,故往往只能定量地控制其中一类错误,而无法有效控制另一类错误.文章从两类错误定义出发,先针对门限参数μ和尺度参数θ分别构造合适的统计量,证明了其在一定条件下分别服从自由度为2和自由度为2n-2的卡方分布,结合卡方分位数得到两类错误与样本容量之间的数量关系.最后,还通过模拟研究论证了本文结论的优良性.In the hypothesis test of two-parameter exponential distribution, when the sample size determined, there is a "trade-off" relationship between the two types of errors. Therefore, only one type of errors can be controlled quantitatively, but the other one cannot be effectively controlled. Based on their definitions, this paper constructed appropriate statistics for threshold parameters and scale parameters, and proved that they obey the Chi-square distribution in two and 2n-2 degrees of freedom respectively in certain conditions, and obtains the quantitative relationship between the two types of errors and sample size using the chi-square quantile.At last, the conclusion is proved by simulation.

关 键 词：门限参数 尺度参数 两类错误 假设检验 

分 类 号：O212.1[理学—概率论与数理统计]