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, ...
where
s > 1 is a parameter and ζ(
s) is
Riemann's
zeta function.
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.
