Zeta distribution

Zeta distribution ( Zipf distribution also to George Kingsley Zipf ) is a discrete probability distribution, the natural numbers x = 1,2,3, ... The probabilities

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

Your -th moment exists if and in this case at

It can be shown that the number of different prime factors of a Zeta - distributed random variable, in turn, are independent random variables. This is the case with any other probability distribution.

To motivate this distribution see Zipfsches law.