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Modeling Particle Size Distribution in Lunar Regolith via a Central Limit Theorem for Random Sums

Author

Listed:
  • Andrey Gorshenin

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia)

  • Victor Korolev

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia
    Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia)

  • Alexander Zeifman

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia
    Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia)

Abstract

A version of the central limit theorem is proved for sums with a random number of independent and not necessarily identically distributed random variables in the double array limit scheme. It is demonstrated that arbitrary normal mixtures appear as the limit distribution. This result is used to substantiate the log-normal finite mixture approximations for the particle size distributions of the lunar regolith. This model is used as the theoretical background of the two different statistical procedures for processing real data based on bootstrap and minimum χ 2 estimates. It is shown that the cluster analysis of the parameters of the proposed models can be a promising tool for revealing the structure of such real data, taking into account the physico-chemical interpretation of the results. Similar methods can be successfully used for solving problems from other subject fields with grouped observations, and only some characteristic points of the empirical distribution function are given.

Suggested Citation

  • Andrey Gorshenin & Victor Korolev & Alexander Zeifman, 2020. "Modeling Particle Size Distribution in Lunar Regolith via a Central Limit Theorem for Random Sums," Mathematics, MDPI, vol. 8(9), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1409-:d:402908
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    Cited by:

    1. Andrey Gorshenin & Victor Kuzmin, 2022. "Statistical Feature Construction for Forecasting Accuracy Increase and Its Applications in Neural Network Based Analysis," Mathematics, MDPI, vol. 10(4), pages 1-21, February.

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