A Moment Preserving Finitization Across the Power Series Family of Probability Distributions

作者：Levy Martin S; Cochran James J^*; Golnabi Saeed

来源：Communications in Statistics - Theory and Methods, 2012, 41(4): 653-664.

DOI：10.1080/03610926.2010.529536

• Finitization
• Moments
• Poisson distribution
• Power series family of distributions
• Taylor series expansion

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.

• 出版日期2012