Abstract
The probability mass function ( PMF ) and the cumulative distribution function ( CDF ) of the generalized binomial distribution ( E(k,n,p) and B(k,n,p) ) are shown to be governed by binary recursive relations similar to those of the binomial coefficient and the k-out-of-n system reliability/unreliability. It is possible to compute E(k,n,p) and B(k,n,p) via computer implementations of recursive functions that are directly based on the aforementioned recursive relations. However, such implementations are highly demanding in both time and space. Alternatively, the recursive relations of E(k,n,p) and B(k,n,p) are given nice interpretations in terms of very regular signal flow graphs, based on which efficient iterative algorithms for computing the set of values E(k,n,p), 0 ≤ k ≤ n, and B(k,n,p), 0 ≤ k ≤ (n−1), for any specific n ≥ 0, are developed. In the worst case, the temporal and spatial complexities of these algorithms are quadratic and linear, respectively, in the number of trials n pertaining to the underlying distribution.