Zeta distribution
The zeta distribution is any of a certain parametrized family of discrete probability distributions whose support is the set of positive integers. It can be defined by saying that if X is a random variable with a zeta distribution, then
- P(X=x) = x-s/ζ(s) for x = 1, 2, 3, ...
It can be shown that these are the only probability distributions for which the multiplicities of distinct prime factors of X are independent random variables.
Some applied statisticians have used the zeta distribution to model various phenomena; see the article on Zipf's law.
