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基于分位数函数和Bootstrap分布的不确定度评定研究

         

摘要

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.%最大信息熵方法是基于概率分布评定测量不确度的主要方法之一。其所依赖的高阶矩需要较大样本的测量数据,而校准/检测实验室的测量一般为小样本,故用最大熵方法评定小样本测量不确定度缺乏一定的可靠性。提出了基于分位数函数和概率权重矩作为约束条件的最大信息熵不确定度评定法,把矩的计算从高次降为一次,并结合遗传算法求解概率分布,用Bootstrap分布估计扩展不确定度和包含区间,解决了由分位数区间估计分布不对称所致的复杂计算问题。

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