The new rank-based concentration index: Further analysis and properties

Area of Science:

• Economics
• Statistics
• Market Analysis

Background:

• The Q index, a sum of quadratic proportions, is widely used for market concentration.
• A novel concentration index, CK, has been introduced, incorporating both proportion distribution and ranks.
• CK is proposed as a superior alternative to Q for various measurement applications.

Purpose of the Study:

• To explore additional properties and generalizations of the CK concentration index.
• To demonstrate CK's mathematical properties, including convexity and decomposition capability.
• To analyze CK's sensitivity to changes in proportion distributions and compare it with other indices.

Main Methods:

• Mathematical analysis to prove CK's convexity.
• Derivation of CK's numbers equivalent and probability interpretation.
• Numerical comparisons and statistical inference procedures.

Main Results:

• CK is proven to be a convex function, enabling decomposition analysis.
• The sensitivity and transfer effects of CK were analyzed.
• Generalizations of CK were developed, and its performance was compared numerically with other indices.

Conclusions:

• CK offers a robust and versatile alternative to existing concentration indices like Q.
• The study provides a comprehensive analysis of CK's properties and potential applications.
• CK demonstrates effectiveness across diverse scenarios, including those with missing small proportions.