Analysis of basic probability distributions, their properties and use in determining type B evaluation of measurement uncertainties

The present paper provides a circumstantial analysis of all basic probability distributions from the point of view of their properties and their use for the determination of measurement uncertainties by using type B evaluation methods. A special attention is devoted to four non-normal probability distributions Di (rectangular distribution, triangular or Simpson’s distribution, bimodal triangular distribution and trapezoidal distribution) and to the family of U(c)-distributions, often called horseshoe distributions. All these distributions are mutually compared and for all of them the coverage factors kp,Di at the confidence level p are calculated including the solution of the inverse problem, i.e. the calculation of the p-values associated with the typical coverage factors kp = 1, 2 and 3 together with the calculation of so called maximum allowable values of kp – denoted as MAV-values – separately for each of mentioned probability distributions Di. These MAV-values are related with the limit situation when the particular probability distribution Di, is fully covered. The use of all tables is demonstrated on numerical examples. Therefore, the present paper provides all tools for a correct attributing such a coverage factor that may be justified in determining a type B evaluation of measurement uncertainty associated with the investigated input quantity Xi following the prescribed probability distribution Di. In this sense, problems formulated in Cl. 2.3.5, NOTE 2 of GUM [1], are quite removed and the correctness of the final solution of uncertainty problem fully justified.

► Xhaustive analysis of all basic probability distributions D used in determining type B evaluation. ► Derivation of formulas for coverage factors at confidence level p and solution of inverse problem. ► Tables of numerical values of coverage factors kp, MAV-values and confidence levels for given kp. ► Removing the problem formulated in Cl. 2.3.5, NOTE 2 of GUM [1].