Abstract:
Let n groups of particles (s particles in group) be placed independently in N cells
and probabilities of all dispositions are equal. Let μ0 be the number of empty cells.
Convergence of moments of distribution of (Dμ0)−1/2(μ0−Eμ0) to the moments of standard
normal distribution is proved.
Citation:
V. G. Mikhaǐlov, “Asymptotic normality of the number of empty cells for group
placing of particles”, Teor. Veroyatnost. i Primenen., 25:1 (1980), 83–91; Theory Probab. Appl., 25:1 (1980), 82–90
\Bibitem{Mik80}
\by V.~G.~Mikha{\v\i}lov
\paper Asymptotic normality of the number of empty cells for group
placing of particles
\jour Teor. Veroyatnost. i Primenen.
\yr 1980
\vol 25
\issue 1
\pages 83--91
\mathnet{http://mi.mathnet.ru/tvp987}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=560059}
\zmath{https://zbmath.org/?q=an:0455.60015|0423.60010}
\transl
\jour Theory Probab. Appl.
\yr 1980
\vol 25
\issue 1
\pages 82--90
\crossref{https://doi.org/10.1137/1125007}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980LG24200007}
Linking options:
https://www.mathnet.ru/eng/tvp987
https://www.mathnet.ru/eng/tvp/v25/i1/p83
This publication is cited in the following 13 articles:
Carina Betken, Christoph Thäle, “Approaching the coupon collector's problem with group drawings via Stein's method”, J. Appl. Probab., 60:4 (2023), 1352
M. G. Chebunin, “Estimating a Number of Cells via a Number of Occupied Ones under Random Choice”, J. Math. Sci., 213:6 (2016), 795–801
Zhang Tong, Hosam M. Mahmoud, “An Urn Model for Population Mixing and the Phases Within”, Methodol Comput Appl Probab, 15:3 (2013), 683
Saidbek S. Mirakhmedov, Sherzod M. Mirakhmedov, “On Asymptotic Expansion in the Random Allocation of Particles by Sets”, J Theor Probab, 23:3 (2010), 904
Hosam M. Mahmoud, “Gaussian phases in generalized coupon collection”, Advances in Applied Probability, 42:4 (2010), 994
Srinivasan Balaji, Hosam Mahmoud, Zhang Tong, “Phases in the Diffusion of Gases via the Ehrenfest URN Modelx”, Journal of Applied Probability, 47:3 (2010), 841
Srinivasan Balaji, Hosam Mahmoud, Zhang Tong, “Phases in the Diffusion of Gases via the Ehrenfest URN Modelx”, J. Appl. Probab., 47:03 (2010), 841
Hosam M. Mahmoud, “Gaussian phases in generalized coupon collection”, Adv. Appl. Probab., 42:04 (2010), 994
V. G. Mikhailov, “Limit theorems for a random covering of a finite setand for the number of solutions of a system of random equations”, Theory Probab. Appl., 41:2 (1997), 265–274
Wolfgang Stadje, “The collector's problem with group drawings”, Advances in Applied Probability, 22:4 (1990), 866
Wolfgang Stadje, “The collector's problem with group drawings”, Adv. Appl. Probab., 22:04 (1990), 866
V. A. Vatutin, V. G. Mihaǐlov, “Limit theorems for the number of empty cells in the equiprobable scheme of group disposal of particles”, Theory Probab. Appl., 27:4 (1983), 734–743
V. G. Mikhailov, “Convergence to the multidimensional normal law in an equiprobable scheme of distributing particles by groups”, Math. USSR-Sb., 39:2 (1981), 145–167
Citation in format AMSBIB
Contact us: