二项分布中成功概率的贝叶斯序贯检验方法

韩峰; 陆希成; 刘钰; 王建国

二项分布中成功概率的贝叶斯序贯检验方法

西北核技术研究所第五研究室,西安 710024

计量
- 文章访问数: 2202
- HTML浏览量: 105
- PDF量: 1541
- 被引次数: 0
出版历程
- 收稿日期: 2012-02-29
- 刊出日期: 2013-02-28

Bayesian sequential test method for probability of success of binomial distribution based on posterior probability

Department of No.5, Northwest Institute of Nuclear Technology, Xi'an 710024, China

摘要

摘要: 针对成败型效应实验研究中二项分布未知参数(成功概率)的假设检验问题,在复杂假设条件下,提出了一种基于Bayesian验后概率的序贯检验方法,建立了检验的判别准则,给出了判别准则临界值的计算方法.在给定截尾实验次数的条件下,提出了一种截尾方案,建立了截尾判断方法.最后结合示例,对上述方法的应用过程进行了说明,并和现有方法进行了分析比较.结果表明:在一定先验信息的条件下,该方法给出的检验样本量远小于经典方法确定的检验样本量.
- 序贯检验 /
- 成功概率 /
- 二项分布 /
- 贝叶斯方法 /
- 截尾方法
Abstract: A sequential test method based on Bayesian posterior probability was proposed to perform tests of hypotheses about probability of success of binomial distribution in complicated hypothesis conditions. The decision rules were constructed and the method for calculating the criterion value was given. For a given maximal sample size, the truncated method of the judge criteria was discussed for hypothesis test. At last, an example illustrated the proposed method and the result was compared with classical methods. The result shows that the sample number determined by the proposed method can be much smaller than that determined by classical methods on the condition of given prior probability.
- sequential test /
- probability of success /
- binomial distribution /
- Bayesian method /
- truncated method

HTML

参考文献(15)

[1]	李科,马弘舸,周海京.微波效应实验最小样本量估计分析[J].强激光与粒子束,2009,21(4):541-544. LI Ke,MA Hongge,ZHOU Haijing.Estimating analysis of least sample of microwave effects experiment[J].High Power Laser and Particle Beams,2009,21(4):541-544.(in Chinese)
[2]	韩峰,王建国,乔登江.对数正态分布场合下产品加固性能的Bayes评估方法[J].应用概率统计,2009,25(4):433-440. HAN Feng,WANG Jianguo,QIAO Dengjiang.Bayesian assessment for product's radiation hardening performance under lognormal distribution[J].Chinese Journal of Applied Probability and Statistics,2009,25(4):433-440.(in Chinese)
[3]	陈家鼎.序贯分析[M].北京:北京大学出版社,1995.
[4]	陈希儒,倪国煦.数理统计学教程[M].合肥:中国科学技术大学出版社,2009.
[5]	周源泉,翁朝曦.可靠性评定[M].北京:科学出版社,1990.
[6]	郭维长.论火工装置的抽样试验与可靠性评估问题[J].中国空间科学,1999,19(3):51-57. GUO Weichang.Study on sampling test and reliability evaluation of pyrotechnical devices[J].Chinese Space Science and Technology,1999,19(3):51-57.(in Chinese)
[7]	武小悦,刘琦.装备试验与评价[M].北京:国防工业出版社,2008.
[8]	夏群力,郭涛,李然.导弹产品的可靠性检验研究[J].系统工程与电子技术,2008,30(3):577-580. XIA Qunli,GUO Tao,LI Ran.Study of reliability test evaluation of missile products[J].Systems Engineering and Electronics,2008,30(3):577-580.(in Chinese)
[9]	张金槐,唐学梅.Bayes方法[M].长沙:国防科技大学出版社,1989.
[10]	张金槐.落点散布鉴定中Bayes 序贯截尾方法的运用[J].国防科技大学学报,1999,21(4):108-113. ZHANG Jinhuai.The research of Bayesian sequential truncated dispersion detecting algorithm of the reentry vehicle's fall points[J].Journal of National University of Defense Technology,1999,21(4):108-113.(in Chinese)
[11]	王国玉,申绪涧,汪连栋,等.电子系统小子样试验理论方法[M].北京:国防工业出版社,2003.
[12]	邢云燕,武小悦.指数分布下可靠性指标验证的截尾SPOT方法[J].系统工程与电子技术,2006,28(8):1282-1284. XING Yunyan ,WU Xiaoyue.Censored SPOT method for reliability index verification under exponential distribution[J].Systems Engineering and Electronics,2006,28(8):1282-1284.(in Chinese)
[13]	董博超,宋保维,梁庆卫,等.武器装备小子样维修性试验与评定方法研究[J].兵工学报,2011,32(3):327-330. DONG Bochao,SONG Baowei,LIANG Qingwei,et.al.Research on small sample maintainability experimentation and evaluation of weapon system[J].Acta Armamentarii,2011,32(3):327-330.(in Chinese)
[14]	刘琦,王囡.基于验后概率的Bayesian序贯方差检验技术(Ⅰ)[J].航空动力学报,2011,26(7):1531-1536. LIU Qi,WANG Nan.Bayesian sequential variance test technique based on posterior probability(Ⅰ)[J].Journal of Aerospace Power,2011,26(7):1531-1536.(in Chinese)
[15]	刘琦,王囡.基于验后概率的Bayesian序贯方差检验技术(Ⅱ)[J].航空动力学报,2011,26(7):1537-1542. LIU Qi,WANG Nan.Bayesian sequential variance test technique based on posterior probability(Ⅱ)[J].Journal of Aerospace Power,2011,26(7):1537-1542.(in Chinese)