- Logarithmic Series Distribution

The probability mass function of a logarithmic series distribution with parameter θ is given by

P (X = k) = aθk

k , 0 < θ < 1, k = 1, 2, . . . ,

where a = −1/[ln(1− θ)]; the cumulative distribution function is given by

F (k|θ) = P (X ≤ k|θ) = a k∑ i=1

θk

k , 0 < θ < 1, k = 1, 2, . . . .