Bounds on the Tail Probability and Absolute Difference Between Two Distributions

Abstract

A fractional moment bound on the tail probabilities of a distribution is proposed and illustrated with examples. It is then combined with the moment bound of Philips–Nelson, resulting in an improvement over the latter. Two bounds on the absolute difference between two distributions, namely the fractional moment and entropy based bounds are introduced. The first compares well with Lindsay–Basak's window function while the second can be made as precise as desired, according to the number of common moments assumed.

Keywords:

• Entropy
• Fractional moments
• Moments
• Tail probability