A generalized binomial distribution

A new generalization of the binomial distribution is introduced that allows dependence between trials, nonconstant probabilities of success from trial to trial, and which contains the usual binomial distribution as a special case. Along with the number of trials and an initial probability of ‘success’, an additional parameter that controls the degree of correlation between trials is introduced. The resulting class of distributions includes the binomial, unirnodal distributions, and bimodal distributions. Formulas for the moments, mean, and variance of this distribution are given along with a method for fitting the distribution to sample data.