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Determination of the Sample Distribution Law by Analysis of Multiple Measurements

Eugene O. Podchasov and Arina D. Terenteva
Department of robotics and complex automation, BMSTU, Russia

Abstract—Determination of distribution law of measured series of values is important task in automated regulation and active control. In many cases this is a challenge, especially when type of the law is uncommon and differ from Gaussian. The method for determination of distribution law based on criteria of process stabilizing is proposed. The recommendation for Poisson, Exponential and χ2 laws are given. Determination of distribution law of series is based on calculation of 4 criteria, each one being based on Mean, standard deviation or its derivative. In each case the series of 1000 computational experiments being held and on base of its results the distribution law being determined. Each case being described by the number of measurements that is necessary for each criteria level stabilize below value of 0,1. It is shown that for each main distribution laws the order in which each criteria stabilize in sequential measurement differs. The order of such stabilization is offered as a way to determine the distribution laws for measurements in active control algorithms, while the measurement amount necessary for stabilization may be used for estimation of distribution laws parameters. The calculation experiment results for some of the most common laws is given and criteria for each law definition is formulated.

Index Terms— mechanical experiment, technical measurement, precision, control automation, consecutive analysis

Cite: Eugene O. Podchasov and  Arina D. Terenteva, "Determination of the Sample Distribution Law by Analysis of Multiple Measurements," International Journal of Mechanical Engineering and Robotics Research, Vol. 10, No. 2, pp. 92-98, February 2021. DOI: 10.18178/ijmerr.10.2.92-98

​Copyright © 2021 by the authors. This is an open access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0), which permits use, distribution and reproduction in any medium, provided that the article is properly cited, the use is non-commercial and no modifications or adaptations are made.