Narrow Results

This paper proposes an unconventional method (PMM) for evaluating the uncertainty of the estimator of measurand value obtained from the non-Gaussian distributed samples of measurement data with a priori partial description (unknown PDF). This method of statistical estimation is based on the apparatus of stochastic polynomial maximization and uses the higher-order statistics (moment and cumulant description) of random variables. The analytical expressions for estimates of uncertainty, obtained with use the polynomial of the degree r = 2 for samples from population of asymmetrical pdf and degree r = 3 — for symmetrical pdf, are given. It is shown that these uncertainties are generally smaller than the uncertainty based only on the arithmetic average, as it is in GUM. Reducing the value of estimated uncertainty of measurement depends on the skewness and kurtosis of samples from asymmetrical pdf or on kurtosis and six order moment of samples from symmetrical pdf. The results of statistical modeling carried out on the basis of the Monte Carlo method confirm the effectiveness of the proposed approach.