Determining the Roots of a Hypergeometric Polynomial

• Activity Number: 680
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Bruce Barrett*+
• Companies: The University of Alabama
• Keywords: hypergeometric ; poisson binomial ; polynomial roots

Abstract

A hypergeometric random variable can be expressed as the sum of independent Bernoulli random variables with distinct success probabilities, pi. These pi are known to be the real roots of a hypergeometric polynomial, that is, a polynomial whose coefficients are the event probabilities from a corresponding hypergeometric pdf. In practice, the roots are determined by numerical methods, which tend to break down for larger polynomials. In this paper we discuss strategies for extending the size of problems that can be solved numerically. We further derive analytical solutions for certain special cases and propose the existence of a general analytical solution.