Abstract:
A non-conventional approach to finding estimates of the result of multiple measurements for a random error
model in the form of bimodal mixtures of exponential distributions is proposed. This approach is based on the
application of the Polynomial Maximization Method (PMM) with the description of random variables by
higher order statistics (moment & cumulant). The analytical expressions for finding estimates and analysis
accuracy to the degree of the polynomial r = 3 are presented. In case when the degree of the polynomial r = 1
and r = 2 (for symmetrically distributed data) polynomial estimate equivalent can be estimated as a mean (average
arithmetic). In case when the degree of the polynomial r = 3, the uncertainty of the polynomial estimate
decreases. The reduction coefficient depends on the values of the 4th and 6th order cumulant coefficients that
characterize the degree of difference while the distribution of sample data from the Gaussian model.
By means of multiple statistical tests (Monte Carlo method), the properties of the normalization of polynomial
estimates are investigated and a comparative analysis of their accuracy with known estimates (mean, median
and center of folds) is made. Areas that depend on the depth of antimodality and sample size, in which
polynomial estimates (for r = 3) are the most effective.
