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 solutions appear to lag behind the needs of modern-age analytics. Motivated by this gap, this paper proposes an alternative solution that is mathematically intuitive, computationally efficient, equivalent to the existing solutions for “standard” cases, while 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.