Family of Pearson discrete distributions generated by the univariate hypergeometric function 3F2(α1, α2, α3; γ1, γ2; λ)

In this work we present a study of the Pearson discrete distributions generated by the hypergeometric function ₃F₂(α₁, α₂, α₃;γ₁, γ₂; λ), a univariate extension of the Gaussian hypergeometric function, through a constructive methodology. We start from the polynomial coefficients of the difference equation that lead to such a function as a solution. Immediately after, we obtain the generating probability function and the differential equation that it satisfies, valid for any admissible values of the parameters. We also obtain the differential equations that satisfy the cumulants generating function, moments generating function and characteristic function, From this point on, we obtain a relation in recurrences between the moments about the origin, allowing us to create an equation system for estimating the parameters by the moment method. We also establish a classification of all possible distributions of such type and conclude with a summation theorem that allows us study some distributions belonging to this family. © 1997 by John Wiley & Sons, Ltd.