A Comparison of the Moment and Factorial Moment Bounds for Discrete Random Variables

Abstract

In this note, we establish the superiority of the factorial moment bound over the moment bound for nonnegative integer-valued discrete random variables. This solves a problem given earlier. We use some results from approximation theory/ numerical analysis to compare the bounds.

Keywords:

• Divided differences
• Interpolation error
• Moment generating function
• Polynomial interpolation
• Survivor/ tail probability