Moment-Based Approximations of Discrete Probability Distributions Using Rational Functions

Abstract

Provost et al. (2009) introduced an approximation to discrete probability mass functions using a base density function and a polynomial function multiplier. In this article, we examine a new estimator constructed by using a rational function multiplier. The new approximation requires fewer moments to calculate, and generally performs better. Several example cases will be presented.

Keywords:

• Approximation
• Moments
• Probability mass function
• Rational function

Mathematics Subject Classification:

• Primary 62E17
• Secondary 60E99

Acknowledgement

The authors would like to acknowledge the contributions of Dr. Steve From to this research, Dr. From's insight and guidance made the above presented work possible.