On the definition of a concentration function relevant to the ROC curve

TL;DR

This paper critiques a recent definition of a concentration function for supervised classification and proposes an alternative, discussing its motivation and relevance within the existing literature.

Contribution

It introduces a new definition of a concentration function for ROC analysis and provides a rationale for its adoption over previous definitions.

Findings

Proposes a different concentration function definition

Motivates the new definition with literature review

Engages with existing ROC analysis frameworks

Abstract

This is a reader's reaction to a recent paper by E. Schechtman and G. Schechtman (Metron, 2019) about the correct definition of a concentration function for the diagnostic, i.e. supervised classification, problem. We propose and motivate a different definition and refer to the relevant literature.