Limit laws for a class of diminishing urn models.
In this work we analyze a class of diminishing 2×2 Pólya-Eggenberger urn models with ball replacement matrix M given by $M= \binom{ -a \,0}{c -d}, a,d∈\mathbb{N}$ and $c∈\mathbb{N} _0$. We obtain limit laws for this class of 2×2 urns by giving estimates for the moments of the considered random varia...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2007-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3519/pdf |
| _version_ | 1797270407621902336 |
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| author | Markus Kuba Alois Panholzer |
| author_facet | Markus Kuba Alois Panholzer |
| author_sort | Markus Kuba |
| collection | DOAJ |
| description | In this work we analyze a class of diminishing 2×2 Pólya-Eggenberger urn models with ball replacement matrix M given by $M= \binom{ -a \,0}{c -d}, a,d∈\mathbb{N}$ and $c∈\mathbb{N} _0$. We obtain limit laws for this class of 2×2 urns by giving estimates for the moments of the considered random variables. As a special instance we obtain limit laws for the pills problem, proposed by Knuth and McCarthy, which corresponds to the special case $a=c=d=1$. Furthermore, we also obtain limit laws for the well known sampling without replacement urn, $a=d=1$ and $c=0$, and corresponding generalizations, $a,d∈\mathbb{N}$ and $c=0$. |
| first_indexed | 2024-04-25T02:03:47Z |
| format | Article |
| id | doaj.art-368f011986a84decaecbcaf103f13dfc |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:47Z |
| publishDate | 2007-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-368f011986a84decaecbcaf103f13dfc2024-03-07T14:34:52ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502007-01-01DMTCS Proceedings vol. AH,...Proceedings10.46298/dmtcs.35193519Limit laws for a class of diminishing urn models.Markus Kuba0Alois Panholzer1Institut für Diskrete Mathematik und Geometrie [Wien]Institut für Diskrete Mathematik und Geometrie [Wien]In this work we analyze a class of diminishing 2×2 Pólya-Eggenberger urn models with ball replacement matrix M given by $M= \binom{ -a \,0}{c -d}, a,d∈\mathbb{N}$ and $c∈\mathbb{N} _0$. We obtain limit laws for this class of 2×2 urns by giving estimates for the moments of the considered random variables. As a special instance we obtain limit laws for the pills problem, proposed by Knuth and McCarthy, which corresponds to the special case $a=c=d=1$. Furthermore, we also obtain limit laws for the well known sampling without replacement urn, $a=d=1$ and $c=0$, and corresponding generalizations, $a,d∈\mathbb{N}$ and $c=0$.https://dmtcs.episciences.org/3519/pdfpólya urnsdiminishing urnspills problemsampling without replacement[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds][info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co][info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| spellingShingle | Markus Kuba Alois Panholzer Limit laws for a class of diminishing urn models. Discrete Mathematics & Theoretical Computer Science pólya urns diminishing urns pills problem sampling without replacement [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| title | Limit laws for a class of diminishing urn models. |
| title_full | Limit laws for a class of diminishing urn models. |
| title_fullStr | Limit laws for a class of diminishing urn models. |
| title_full_unstemmed | Limit laws for a class of diminishing urn models. |
| title_short | Limit laws for a class of diminishing urn models. |
| title_sort | limit laws for a class of diminishing urn models |
| topic | pólya urns diminishing urns pills problem sampling without replacement [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| url | https://dmtcs.episciences.org/3519/pdf |
| work_keys_str_mv | AT markuskuba limitlawsforaclassofdiminishingurnmodels AT aloispanholzer limitlawsforaclassofdiminishingurnmodels |