Editing Yule–Simon distribution (section)

==Generalizations==

The two-parameter generalization of the original Yule distribution replaces the beta function with an [[incomplete beta function]].  The probability mass function of the generalized Yule–Simon(''&rho;'', ''&alpha;'') distribution is defined as

:<math>
 f(k;\rho,\alpha) = \frac \rho {1-\alpha^\rho} \;
 \mathrm{B}_{1-\alpha}(k, \rho+1),
 \,</math>

with <math>0 \leq \alpha < 1</math>.  For <math>\alpha = 0</math> the ordinary Yule–Simon(''&rho;'') distribution is obtained as a special case. The use of the incomplete beta function has the effect of introducing an exponential cutoff in the upper tail.