Using a two-sided power distribution family in processing measurement results

When processing measurement results and evaluating their accuracy, a normal distribution is traditionally used; however, in some cases this approach may be incorrect (for example, if the distribution is significantly asymmetric or it is bounded). Therefore, the selection of a family of distributions is relevant, which would allow the approximation of both traditionally applied normal and uniform laws, as well as encompass distributions of other types that more adequately reflect the specifics of particular measurement tasks. To model measurement data and evaluate accuracy indicators, it is proposed to use the family of two-sided power distributions. The choice of this family is due to the fact that it is described by an extremely simple mathematical model while providing sufficient variety of probability density function shapes, including uniform, bimodal, and unimodal distributions (both symmetric and asymmetric). Methods for fitting (assigning) the distribution law are provided based on both a priori information (using specified accuracy indicators: measured value, standard or expanded uncertainties, coverage interval boundaries for a given probability level) and sample data (including maximum likelihood, the method of moments, and two-sided power distribution fitting via inverse transformation). Metrologically justified criteria for the approximation of continuous distributions by distributions of the family under consideration are proposed, and its application in evaluating the uncertainty of multiple equally precise measurements is described. Software has been developed for transforming distributions, which allows the measurement model to be specified in an analytical form. The results obtained are useful for specialists applying statistical modeling methods when evaluating measurement results, certifying measurement procedures, and processing data from interlaboratory comparisons.