High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the zeta distribution is a discrete probability distribution. If X is a zeta-distributed random variable with parameter s, then the probability that X takes the integer value k is given by the probability mass function f_s(k)=k^{-s}/zeta(s), where (s) is the Riemann zeta function (which is undefined for s = 1)..The series on the right is just a series representation of the Riemann zeta function, but it only converges for values of s-n that are greater than unity.