Geodesic
Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 913-922

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We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak convergence to a two-dimensional Gaussian process. Its covariance function depends only on exponent of regular decrease of probabilities. We obtain parameter estimates that have a normal asymototics for its joint distribution together with forward and backward processes. We use these estimates to construct statistical tests for the homogeneity of the urn scheme on the number of thrown balls.
Keywords: Zipf's law, weak convergence, Gaussian process, statistical test. 
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     author = {M. G. Chebunin and A. P. Kovalevskii},
     title = {Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {913--922},
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     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a27/}
}
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M. G. Chebunin; A. P. Kovalevskii. Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 913-922. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a27/