Geodesic
Convergence rate estimators for the number of ones in outcome sequence of MCV generator with $m$-dependent registers items
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 18-25

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This paper is focused on studying properties of the number of ones $\xi_{r}$ in outcome sequence of MCV generator with $r$ registers over $GF(2).$ We concern on the case when generator outcome sequence has length close to the cycle length and registers filled with $m$-dependent binary random variables. Exact expressions for mean and variance of ${{\xi }_{r}}$ are given. We derive estimate in uniform metric between cumulative distribution functions of the standardized number of ones in MCV generator outcome sequence and product of $r$ independent standard normal random variables. The estimate allows to prove limit theorem for ${{\xi }_{r}}$ when number $r$ is fixed. We also estimate distance (in uniform metric) between the cumulative distribution function of normalized $\xi_{r}$ and log-normal distribution law. This result allows to prove a normal-type limit theorem for $r\to \infty$.
Keywords: MCV generator, normal-type limit theorem, uniform distance estimate, m-dependent random variables. 
@article{SEMR_2014_11_a29,
     author = {N. M. Mezhennaya},
     title = {Convergence rate estimators for the number of ones in outcome sequence of {MCV} generator with $m$-dependent registers items},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {18--25},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a29/}
}
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N. M. Mezhennaya. Convergence rate estimators for the number of ones in outcome sequence of MCV generator with $m$-dependent registers items. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 18-25. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a29/