Distribution of the combinatorial multisets component vectors
We explore a class of random combinatorial structures called weighted multisets. Their components are taken from an initial set satisfying general boundedness conditions posed on the number of elements with a given weight. The component vector of a multiset of weight n taken with equal probability h...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2012-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/14874 |
| _version_ | 1811311388950265856 |
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| author | Eugenijus Manstavičius Robertas Petuchovas |
| author_facet | Eugenijus Manstavičius Robertas Petuchovas |
| author_sort | Eugenijus Manstavičius |
| collection | DOAJ |
| description | We explore a class of random combinatorial structures called weighted multisets. Their components are taken from an initial set satisfying general boundedness conditions posed on the number of elements with a given weight. The component vector of a multiset of weight n taken with equal probability has dependent coordinates, nevertheless, up to r = o(n) of them as n→∞, we approximate by an appropriate vector comprised from independent negative binomial random variables. The main result is an estimate of the total variation distance. |
| first_indexed | 2024-04-13T10:16:59Z |
| format | Article |
| id | doaj.art-fe37417393914c558b402b622bda35fe |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-04-13T10:16:59Z |
| publishDate | 2012-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-fe37417393914c558b402b622bda35fe2022-12-22T02:50:40ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2012-12-0153A10.15388/LMR.A.2012.12Distribution of the combinatorial multisets component vectorsEugenijus Manstavičius0Robertas Petuchovas1Vilnius UniversityVilnius UniversityWe explore a class of random combinatorial structures called weighted multisets. Their components are taken from an initial set satisfying general boundedness conditions posed on the number of elements with a given weight. The component vector of a multiset of weight n taken with equal probability has dependent coordinates, nevertheless, up to r = o(n) of them as n→∞, we approximate by an appropriate vector comprised from independent negative binomial random variables. The main result is an estimate of the total variation distance.https://www.journals.vu.lt/LMR/article/view/14874Random combinatorial multisetnegative binomial distributionadditive functioncentral limit theorem |
| spellingShingle | Eugenijus Manstavičius Robertas Petuchovas Distribution of the combinatorial multisets component vectors Lietuvos Matematikos Rinkinys Random combinatorial multiset negative binomial distribution additive function central limit theorem |
| title | Distribution of the combinatorial multisets component vectors |
| title_full | Distribution of the combinatorial multisets component vectors |
| title_fullStr | Distribution of the combinatorial multisets component vectors |
| title_full_unstemmed | Distribution of the combinatorial multisets component vectors |
| title_short | Distribution of the combinatorial multisets component vectors |
| title_sort | distribution of the combinatorial multisets component vectors |
| topic | Random combinatorial multiset negative binomial distribution additive function central limit theorem |
| url | https://www.journals.vu.lt/LMR/article/view/14874 |
| work_keys_str_mv | AT eugenijusmanstavicius distributionofthecombinatorialmultisetscomponentvectors AT robertaspetuchovas distributionofthecombinatorialmultisetscomponentvectors |