Application of finitized power series distributions to accelerate variate generation. Part I: two useful algorithms. (12th May 2018) - Levy, Martin S.; Cochran, James J.; Golnabi, Saeed; Kirtland, James Andrew
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.