指数分布下可靠性参数的推断
Inference of Reliability Parameters under Exponential Distribution
DOI: 10.12677/AAM.2019.89183, PDF,   
作者: 魏秋月, 王春玲：北京建筑大学理学院，北京；赵 昕：北京工商大学嘉华学院，北京
关键词: 指数分布；广义推断；Bootstrap；Bayes；大样本近似估计；Exponential Distribution； Generalized Inference； Bayes； Bootstrap； Large Sample Approximation Estimation
摘要: 本文研究了单参数指数分布下参数 的区间估计方法，给出了单参指数分布中参数 的两种广义枢轴量、参数的广义置信区间的解析解及频率性质理论证明，同时给出了假设检验问题的广义p值，另外给出三种已有方法，即Bayes方法、大样本近似估计方法和Bootstrap重抽样方法，通过Monte Carlo方法对四种方法进行模拟，模拟结果表明：广义推断和Bayes方法的覆盖概率在样本量较小的情况下保持在给定置信水平附近，且平均置信长度较小，另外本文又比较了四种方法对于假设检验问题犯第一类错误概率与检验的势，模拟结果验证了广义推断方法的良好性能。
Abstract: In this paper, we study the interval estimation method of parameter   under single pa-rameter exponential distribution. Two kinds of generalized pivots of parameter   in single parameter exponential distribution, analytical solutions of generalized confidence interval of parameter and theoretical proof of frequency property are given. At the same time, the generalized p value of hypothesis testing problem is given. In addition, three existing methods, namely Bayes method, approximate estimation method of large sample and Bootstrap resampling method are given. Four methods are simulated by Monte Carlo method. The simulation results show that the coverage probability of generalized inference and Bayes method remains near the confidence level when sample size is small, and the average confidence length is smaller. In addition, this paper compares the error 1 probability and the power for hypothesis testing. The simulation results verify the good performance of the generalized inference method.
文章引用：魏秋月, 王春玲, 赵昕. 指数分布下可靠性参数的推断[J]. 应用数学进展, 2019, 8(9): 1562-1573. https://doi.org/10.12677/AAM.2019.89183

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