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

Andrey Gorshenin, Victor Korolev and Alexander Zeifman
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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
Alexander Zeifman: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia

Mathematics, 2020, vol. 8, issue 9, 1-24

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.

Keywords: central limit theorem; random sequence; random index; transfer theorem; random sum; random Lindeberg condition; log-normal mixtures; grouped data; bootstrap; minimizing ?2 estimate; EM algorithm; statistical estimations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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