Odchylky od normálního zákona chyb
On the description and analysis of measurements of continuous quantities
The measurement of continuous quantities is the basis for all mathematical and statistical analysis of phenomena in engineering and science.Therefore a suitable mathematical description of measurement results is basic for realistic analysis methods for such data. Since the result of a measurement of a continuous quantity is not a precise real number but more or less non- precise, it is necessary to use an appropriate mathematical concept to describe measurements. This is possible by the description...
On the Newcomb-Benford law in models of statistical data.
We consider positive real valued random data X with the decadic representation X = Σi=∞∞Di 10i and the first significant digit D = D(X) in {1,2,...,9} of X defined by the condition D = Di ≥ 1, Di+1 = Di+2 = ... = 0. The data X are said to satisfy the Newcomb-Benford law if P{D=d} = log10(d+1 / d) for all d in {1,2,...,9}. This law holds for example for the data with log10X uniformly distributed on an interval (m,n) where m and n are integers. We show that if log10X has a distribution function...