Maximum Feasible Parameter Size for Moment Preserving Finitizations

• Activity Number: 556
• Type: Contributed
• Date/Time: Wednesday, August 3, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Martin Levy* and James J. Cochran and Saeed Golnabi
• Companies: University of Cincinnati and University of Alabama and Optimum Office Solutions
• Keywords: moments ; finitization ; variate simulation ; Taylor series expansion ; discrete probability distributions ; probability models

Abstract

Negative Taylor Series Finitization (NTSF) is a moment preserving method that transforms a power series distribution into one having smaller support of size n with moments coinciding with the first n moments of the parent distribution. A property of an NTSF is that the maximum feasible parameter size (MFPS), i.e., largest parameter yielding a proper distribution, is generally smaller than that of the parent distribution, and a function of n. Determination of the MFPS is needed for NTSF applications such as in fast variate generation. In a previous presentation, based on extensive numerical studies, we issued three conjectures regarding the MFPS. Now, we revisit these, and rigorously prove three corresponding modifications to those claims. That is, under well-defined conditions : 1) The MFPS is determined uniquely via the roots obtained by setting the (n-1)st finitized probability to zero; 2) The MFPS monotonically decreases as a function of increasing n except for the Poisson (where the MFPS is constant for all n); and 3) the Poisson is unique in this regard. We show if there is a violation of the conditions, applying the NTSF method does not yield a probability distribution.