Alternative statistical inference for the first normalized incomplete moment

TL;DR

This paper introduces a new, efficient statistical inference method for the first normalized incomplete moment, enhancing accuracy and applicability in economic and social inequality analysis.

Contribution

It presents an alternative, adaptable inference approach that improves upon existing methods, especially for non-standard cases, with demonstrated theoretical and practical benefits.

Findings

The new method is computationally efficient and mathematically equivalent to standard solutions in typical cases.

It reveals that common industry practices can cause significant challenges for reliable inference.

The approach is validated through simulations and real-world examples.

Abstract

This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference appears to lag behind the needs of modern-age analytics. To fill this gap, we propose an alternative solution that is intuitive, computationally efficient, mathematically equivalent to the existing solutions for "standard" cases, and easily adaptable to "non-standard" ones. The theoretical and practical advantages of the proposed methodology are demonstrated via both simulated and real-life examples. In particular, we discover that a common practice in industry can lead to highly non-trivial challenges for trustworthy statistical inference, or misleading decision making altogether.