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A Moment Preserving Finitization Across the Power Series Family of Probability Distributions
Authors:Martin S Levy  Saeed Golnabi
Institution:1. University of Cincinnati , Cincinnati , Ohio , USA;2. Optimum Office Solutions , Lawrenceville , Georgia , USA
Abstract:Finitization transforms a discrete distribution into a distribution with smaller support of specified size. In special cases finitization preserves moments (moments of the order n finitization coincide with those of the parent distribution). We create a moment preserving finitization method for power series distributions by introducing an alternative representation and showing how to finitize members of this new class in a manner that preserves moments of the parent distribution. We provide results on convolutions and a reproductive property for power series distributions that have been finitized in this manner, and show how these finitized distributions accelerate variate generation in simulation.
Keywords:Finitization  Moments  Poisson distribution  Power series family of distributions  Taylor series expansion
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