WittenBellProbDist.__init__(freqdist, bins=None)[source]

Creates a distribution of Witten-Bell probability estimates. This distribution allocates uniform probability mass to as yet unseen events by using the number of events that have only been seen once. The probability mass reserved for unseen events is equal to T / (N + T) where T is the number of observed event types and N is the total number of observed events. This equates to the maximum likelihood estimate of a new type event occurring. The remaining probability mass is discounted such that all probability estimates sum to one, yielding:

  • p = T / Z (N + T), if count = 0
  • p = c / (N + T), otherwise

The parameters T and N are taken from the freqdist parameter (the B() and N() values). The normalizing factor Z is calculated using these values along with the bins parameter.

  • freqdist (FreqDist) – The frequency counts upon which to base the estimation.
  • bins (int) – The number of possible event types. This must be at least as large as the number of bins in the freqdist. If None, then it’s assumed to be equal to that of the freqdist