International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 60, Pages 3827-3840

On the birthday problem: some generalizations and applications

P. N. Rathie and P. Zörnig

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 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.