By Franco (EDT)/ Forbes, Alistair B. (EDT) Pavese
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Extra resources for Advances in Data Modeling for Measurements in the Metrology and Testing Fields
B. Rossi Note that, as already pointed out by Gauss, the same phenomenon, the residual calibration error θ, gives rise to a systematic error if we consider as ‘observations of the same class’ the indications of a single instrument (index i ﬁxed to, say, i0 ), whilst it becomes a random variation if we sample instruments from the class of all the instrument of the same type (index i varying from 1 to m). Consider the following averages. – Grand average, y¯ = 1/N ij yij , which is an estimate of x.
There are many approaches in the literature to model comparison data26 . However, one can basically summarise them into the two main viewpoints labelled as “Approach A” and “Approach B” in the following applying to 26 For example, [CFH07, DP06, FP06, Gra05, IWM04, Kak04, KDP03, KDP04, KTH06, LW98, LW06, PM82, RV98, SE91, SoSi06, Whi00, Whi04, WI06, Wil06b, Wil06c] and references therein. An Introduction to Data Modelling Principles in Metrology and Testing 17 most relevant cases, with some exceptions summarised below in “Other Approaches”.
Let us consider again the case of repeated measurement, as described by model (5). We still assume that the errors vi are independent and equally distributed, and we also require that their distribution p(v) is symmetric about the origin and has a ﬁnite support. Let x ˆ = y¯ be the selected estimate for x and e=x ˆ−x (9) the estimation error. Then Laplace shows that e is asymptotically normally distributed with a variance proportional to N −1 . So we ﬁnd here another way of deriving the normal distribution: it is the distribution of the estimation error, suitable for long series of observations.