Statistics

    

Arguments in Favor of the Berger-Parker Index as an Effective Sample Size: The Only True Particle Counter

Authors: L. Martino

In many fields, including computational statistics, ecology, economics, and physics, normalized weights define a discrete probability mass function over a set of entities/samples. The effective sample size (ESS) quantifies the concentration of these weights, providing a measure of sample representativeness. In this work, we show that, among various ESS formulations, the Berger-Parker index uniquely preserves the relative proportions of the weights, acting as a true particle counter. Other commonly used ESS expressions tend to overestimate the effective sample size when only normalized weights are considered. Several examples and formal demonstration are provided.

Comments: 13 Pages.

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[v1] 2025-10-12 10:04:53

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