Simple and accurate method to evaluate type a standard and expanded uncertainties of measurement for the Laplace distributed observations

The article proposes and investigates a simple and accurate evaluation of the standard and expanded uncertainty of the Laplace population median. With the number of observations n, the known probability distribution describing the sample median for n-2 observations was used to approximate the uncertainty of the population median. The proposed approximation was tested by comparison with exact results for n ≤ 10 and with the Monte Carlo method. It has been shown that the standard and expanded (confidence level p = 0.90, 0.95, and 0.99) uncertainties determined by the proposed approximation differ from values determined by MCM by less than about 1%. Using the median instead of the mean value as the measurement result provides a measurement uncertainty lower by about 25% when n ≥ 35, and over 29% when n ≥ 70.

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This publication is supported by the Polish Ministry of Education and Science under the program "Regional Initiative of Excellence" in 2019-2023 (project number 027/RID/2018/19.