Abstract
The presence of random errors in measurements leads to the wide usage of the concept of random quantity as a mathematical model for random errors and, equivalently, for measurement results. The realization of the random error in a given act of measurement is called the random error of a separate measurement, and the word “separate” is often omitted for brevity. Where it can cause confusion between a separate measurement and a complete measurement (which may comprise multiple separate measurements), we will refer to the results of separate measurements as observations.
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Notes
- 1.
With a slight abuse of notation, we use x i to denote the i th observation in both a specific sample (where it is just a number) and in a random sample (where it is a random variable).
- 2.
As usual, \(\left\lfloor x \right\rfloor \) denotes the greatest integer equal to or smaller than x and \(\left\lceil x \right\rceil \) stands for the smallest integer equal to or greater than x.
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Rabinovich, S.G. (2013). Statistical Methods for Experimental Data Processing. In: Evaluating Measurement Accuracy. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6717-5_3
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