|
|
|
| Uncertainty Evaluation Based on Quantile Function and Bootstrap |
| SONG Ming-shun, ZHANG Jun-liang, FANG Xing-hua |
| SONG Ming-shun, ZHANG Jun-liang, FANG Xing-hua |
|
|
|
|
Abstract Maximum entropy is one of the chief methods in the evaluation of measurement uncertainty based on probability distribution, and the higher moments it depended on a larger sample of measurement data. However, measurement in calibration and testing laboratories is generally a small sample survey, so evaluation of measurement uncertainty based on the maximum entropy method for small samples lacks a certain degree of reliability. A method for uncertainty evaluation based on quantile function and probability weighting moment is put forward as the constraint condition of maximum information entropy method. By this way, the high order moment is fell down for a moment, the probability distribution is solved with the combination of genetic algorithm, and the complicated calculation problem arising from quantile interval estimation of asymmetric distribution is managed about with Bootstrap distribution estimation for expanded uncertainty and coverage interval.
|
|
|
|
|
|
［1］ Jaynes E T. Information theory and statistical mechanics ［J］. Phys Rev, 1957, 104(6):620-630.
［2］ D′Antona G. Expanded Uncertainty and Coverage Factor Computation by High Order Moment Analysis［C］//IMTC2004-Instrumentation and Measurement Technology Conference. Italy: Institute of Electrical and Electronics Engineers Inc, 2004, 234-238.
［3］ Pandey M D. Direct estimation of quantile functions using the maximum entropy principle［J］. Structural Safety, 2000,22(1): 61-79.
［4］ Greenwood J A, Landwehr J M, Matalas N C, et al. Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form ［J］. Water Resourc Res,1979,15(5):1049-1054.
［5］ Fang X H, Song M S. Estimation of Maximum-entropy Distribution Based on Genetic Algorithms in Evaluation of the Measurement Uncertainty ［C］//2010 Second WRI Global Congress on Intelligent Systems. Wuhan, China: Computer Society, 2010,292-297.
［6］ 方兴华.在测量不确定度评定中用PME确定PDF的研究［D］.杭州:中国计量学院.2009.
［7］ Efron B. Bootstrap methods: another look at the jack-knife ［J］. The Annals of Statistics, 1979, 7(1):1-26.
［8］ Efron B. Nonparametric estimates of standard error and confidence intervals ［J］. The Canadian Journal of Statistics, 1981, 9(2): 137-172.
［9］ Timmerman M E, TerBrak C J F. Bootstrap confidence intervals for principal response curves ［J］. Computational Statistic & Data Analysis, 2008, 52(4):1837-1849.
［10］ 孙永厚, 周洪彪, 黄美发. 基于最大熵的测量不确定度的贝叶斯评估方法［J］.统计与决策,2008, (12):143-145.
［11］ BIPM,IEC,IFCC,ISO,IUPAC,IUPAP,OIML. Guide to the expression of uncertainty in measurement［S］. 2008. |
|
|
|
2014, Vol. 35 
