International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 60, Pages 3827-3840
On the birthday problem: some generalizations and applications
Departamento de Estatística, Instituto de Ciências Exatas, Universidade de Brasília, Brasília, DF 70910-900, Brazil
Received 3 October 2001
Copyright © 2003 P. N. Rathie and P. Zörnig. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 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.