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Theory of Probability and Mathematical Statistics

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Normal limiting distribution of the normalized number of extraneous solutions of a compatible system of nonlinear random equations over the field GF(2)


Authors: V. I. Masol and S. Ya. Slobodyan
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 139-151
MSC (2010): Primary 60C05, 15A52, 60F99
DOI: https://doi.org/10.1090/tpms/955
Published electronically: August 10, 2015
MathSciNet review: 3242026
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Abstract: Conditions are presented under which the distribution of the properly normalized number of extraneous solutions of a system of compatible random equations over the field GF(2) tends to a standard normal distribution.


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Additional Information

V. I. Masol
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine
Email: vimasol@ukr.net

S. Ya. Slobodyan
Affiliation: Department of Statistics and Higher Mathematics, Faculty for Mathematics and Informatics, Vasyl Stefanyk Precarpathian National University, Shevchenko Street, 57, Ivano-Frankivsk, 76018, Ukraine
Email: slobodian_s@ukr.net

DOI: https://doi.org/10.1090/tpms/955
Keywords: Random equations, field GF(2), limiting normal distribution, {extraneous} solutions
Received by editor(s): March 18, 2013
Published electronically: August 10, 2015
Article copyright: © Copyright 2015 American Mathematical Society