Cumulative hypergeometric processes: A statistical role for the \(_ nF_{n-1}\) functions
The authors look at the problem of sampling without replacement leading to a generalization of the classical discrete hypergeometric probability model. The dependence of the probability of success from trial to trial is assumed to be governed by a certain recurrence relation. The distribution function for the number of successes is derived and it is shown that this can be written in terms of a hypergeometric function of the type \({}_ pF_{p-1}\). Several particular situations and limiting cases leading to generalized binomials and negative binomials are also considered.
generalized binomials and negative binomials
scientific article; zbMATH DE number 4098378