# Birthday paradox for non-uniform distributions

The classic birthday paradox considers all $n$ possible choices to be equally likely (i.e. every day is chosen with probability $1/n$) and once $\Omega(\sqrt{n})$ days are chosen, the probability of $2$ being the same, is a constant. I’m wondering if someone could point me to an analysis that also works for a non-uniform distribution of days?

#### Solutions Collecting From Web of "Birthday paradox for non-uniform distributions"

Maybe those can help you (yes, I know this thread is old, but maybe the answer can be useful to someone else)

http://eprint.iacr.org/2010/616.pdf

http://www.ism.ac.jp/editsec/aism/pdf/044_3_0479.pdf