A Polynomial Estimation of Measurand Parameters for Samples of Non-Gaussian Symmetrically Distributed Data

The non-standard method for evaluating of the average and standard deviation of the symmetrically non-Gaussian-distributed data of sample with a priori partial description (unknown PDF) is proposed. This method of statistical estimation is based on the apparatus of stochastic polynomials and uses the higherorder statistics (moment & cumulant description) of random variables. The analytical expressions for finding estimates for the degree of the polynomial s = 3 and their accuracy analyzes are given. It is shown that the uncertainty estimates received for polynomial are generally less than the uncertainty estimates obtained based on the mean (arithmetic average). Reduction factor, which depends on the MSE values of higher order cumulant coefficients, characterizes the degree of the sampling distribution differences from the Gaussian model. The results of statistical modeling, based on the Monte Carlo method, confirmed the effectiveness of the proposed approach are presented.