Application of finitized power series distributions to accelerate variate generation. Part I: two useful algorithms. (12th May 2018)

• Record Type: Journal Article
• Authors: Levy, Martin S.; Cochran, James J.; Golnabi, Saeed; Kirtland, James Andrew
• Is Part Of: International transactions in operational research. Volume 26:Number 6(2019)
• Page Start: 2305
• Page End: 2323
• Publication Date: 2018-05-12
• Subjects: applied probability -- finitization -- method of aliasing -- moments -- probability -- random variate generation -- simulation -- Taylor series expansion -- uncertainty modeling; Operations research -- Periodicals; 003
• DOI: 10.1111/itor.12549
• Languages: English
• ISSNs: 0969-6016

Abstract

Abstract: Negative Taylor Series Finitization ( NTSF ) is a moment preserving method that transforms a power series distribution into another having smaller support of size n with moments coinciding with the first n moments of the parent distribution. We present algorithms for addressing two issues that arise when developing an NTSF . The first is based on the Kolmogorov–Smirnov statistic for choosing n . The second produces the maximum feasible parameter space ( MFPS ), or largest set of parameters yielding a proper distribution, which is necessary because the parameter space of an NTSF distribution is constrained. Both are essential for finitization applications such as fast variate generation. Under well‐defined conditions, (1) the MFPS is determined uniquely via the roots obtained by setting the ( n −1)st finitized probability to 0, (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.