On moment indeterminacy of the Benini income distribution

TL;DR

This paper demonstrates that the Benini income distribution, despite having finite moments, is not uniquely determined by its moments, revealing a moment indeterminacy property similar to related distributions.

Contribution

It establishes that the Benini distribution is not uniquely identified by its moments and provides explicit examples of different distributions sharing the same moments.

Findings

Benini distribution is not determined by its moments

Explicit examples of distributions with identical moments

Related distributions are briefly analyzed

Abstract

The Benini distribution is a lognormal-like distribution generalizing the Pareto distribution. Like the Pareto and the lognormal distributions it was originally proposed for modeling economic size distributions, notably the size distribution of personal income. This paper explores a probabilistic property of the Benini distribution, showing that it is not determined by the sequence of its moments although all the moments are finite. It also provides explicit examples of distributions possessing the same set of moments. Related distributions are briefly explored.