Moments and Entropy of the Interpolating Family of Size Distributions

TL;DR

This paper leverages the tractability of the Interpolating Family distribution to derive explicit formulas for its moments and entropy, unifying several known distributions under a common framework.

Contribution

It provides explicit expressions for moments and entropy of the IF distribution, encompassing many well-known size distributions as special cases.

Findings

Explicit formulas for moments of the IF distribution

Closed-form expression for the differential entropy

Unified framework for various size distributions

Abstract

Sinner et al. (2016) recently introduced a five-parameter family of size distributions, coined Interpolating Family or IF distribution for short. In this complementary note, we take advantage of the tractability of the IF distribution to compute the moments and the differential entropy. As a consequence, we deduce at a single stroke the corresponding expressions for many well-known size distributions arising as special cases of the IF distribution.