On the birthday problem: some generalizations and applications
We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functions U(−;−;−) which are computable using the software Mathematica. The...
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Hindawi Limited
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203110101 |
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doaj-1e934504d57c416a9589b49982753ff82020-11-24T23:19:32ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003603827384010.1155/S0161171203110101On the birthday problem: some generalizations and applicationsP. N. Rathie0P. Zörnig1Departamento de Estatística, Instituto de Ciências Exatas, Universidade de Brasília, Brasília, DF 70910-900, BrazilDepartamento de Estatística, Instituto de Ciências Exatas, Universidade de Brasília, Brasília, DF 70910-900, BrazilWe study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functions U(−;−;−) which are computable using the software Mathematica. The distribution is generalized in two possible directions, one of them consists in considering a random graph with a single attracting center. Possible applications are also indicated.http://dx.doi.org/10.1155/S0161171203110101 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
P. N. Rathie P. Zörnig |
| spellingShingle |
P. N. Rathie P. Zörnig On the birthday problem: some generalizations and applications International Journal of Mathematics and Mathematical Sciences |
| author_facet |
P. N. Rathie P. Zörnig |
| author_sort |
P. N. Rathie |
| title |
On the birthday problem: some generalizations and applications |
| title_short |
On the birthday problem: some generalizations and applications |
| title_full |
On the birthday problem: some generalizations and applications |
| title_fullStr |
On the birthday problem: some generalizations and applications |
| title_full_unstemmed |
On the birthday problem: some generalizations and applications |
| title_sort |
on the birthday problem: some generalizations and applications |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2003-01-01 |
| description |
We study the birthday problem and some possible extensions. We
discuss the unimodality of the corresponding exact probability
distribution and express the moments and generating functions by
means of confluent hypergeometric functions U(−;−;−) which
are computable using the software Mathematica. The distribution
is generalized in two possible directions, one of them consists
in considering a random graph with a single attracting center.
Possible applications are also indicated. |
| url |
http://dx.doi.org/10.1155/S0161171203110101 |
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AT pnrathie onthebirthdayproblemsomegeneralizationsandapplications AT pzornig onthebirthdayproblemsomegeneralizationsandapplications |
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