Breadth Formula in Information Theory and Diversity Metrics #3732988 (License: Personal Use)

This equation defines breadth as the inverse of the sum of squared probabilities \( \sum_{i=1}^{s} p_i^2 \), commonly used in ecology, information theory, and machine learning to assess evenness or concentration. It is closely related to the Simpson index and provides a normalized measure of dispersion-higher breadth indicates greater uniformity among categories. The formula assumes probabilities \( p_i \) sum to 1 and are non-negative.

Used in academic papers, data science tutorials, and statistical modeling guides to explain diversity indices; appears in contexts like species richness analysis, classification confidence, and portfolio risk diversification. Matches user intent for understanding mathematical foundations of entropy-like metrics.