Estimation of Measurand Parameters for Data from Asymmetric Distributions by Polynomial Maximization Method

  • Zygmunt Lech Warsza
  • Serhii Zabolotnii
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 743)


In this paper the non-conventional method for evaluating the standard uncertainty of the estimator of measurand value obtained from the non-Gaussian asymmetrically distributed sampled data with a priori partial description (known only few initial moments, unknown PDF distribution of population) is proposed. This method of statistical estimation is based on the apparatus of maximization the stochastic polynomials (PMM method proposed by Kunchenko [11]) and uses the higher-order statistics (moment or cumulant description) of random variables. The analytical expressions for finding estimates and analyzing their accuracy to the degree of the polynomial s = 2 is given. It is shown that for the asymmetric PDF-s the uncertainty estimates for received polynomial are generally smaller than the uncertainty estimates obtained based on the mean (arithmetic average). Reducing the uncertainty of measurement depends on the skewness and kurtosis. On the basis of the Monte Carlo method statistical modelling is carried out, the results confirm the effectiveness of the proposed approach.


Estimator Non-Gaussian model Stochastic polynomial Means value Variance Skewness and kurtosis 


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Industrial Research Institute for Automation and Measurements PIAPWarsawPoland
  2. 2.Cherkasy State Technological UniversityCherkasyUkraine

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