Probability functions of discrete probability distributions as solutions of the Pearson difference equation for the discrete classical orthogonal polynomials (Q798486)

Using the Pearson difference equation for the discrete classical orthogonal polynomials the difference equations and the Rodrigues formulas are obtained. The resulting weight functions prove to be the probability functions of the most important discrete probability distributions: Pólya distribution from the Hahn and Krawtchouk polynomials, negative binomial distribution from the Meixner polynomials, Poisson distribution from the Charlier polynomials.