AWhat changed
A bell curve may approximate a sum of independent random errors, but an approximation is more useful when its error is bounded. Berry gives a uniform bound on the difference between the cumulative distribution of a sum and its matching Gaussian distribution. His original estimate uses finite third absolute central moments and a maximum moment ratio; in the identically distributed case it gives an inverse-square-root rate in the number of terms. The work turns a limiting statement into a quantitative comparison.
Scientific scope
A bell curve may approximate a sum of independent random errors, but an approximation is more useful when its error is bounded. Berry gives a uniform bound on the difference between the cumulative distribution of a sum and its matching Gaussian distribution. His original estimate uses finite third absolute central moments and a maximum moment ratio; in the identically distributed case it gives an inverse-square-root rate in the number of terms. The work turns a limiting statement into a quantitative comparison. The variates are mutually independent and one-dimensional, with at least one positive variance. The original general bound uses the maximum moment ratio, not the later common sum-of-third-moments expression for nonidentically distributed variables. Uniform distribution-function distance is not density error, relative far-tail accuracy or an assertion that the bound is sharp. The 1.88 constant is the paper's historical upper bound, not the best current constant. Esseen's independent work and later refinements are separate contributions.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The variates are mutually independent and one-dimensional, with at least one positive variance. The original general bound uses the maximum moment ratio, not the later common sum-of-third-moments expression for nonidentically distributed variables. Uniform distribution-function distance is not density error, relative far-tail accuracy or an assertion that the bound is sharp. The 1.88 constant is the paper's historical upper bound, not the best current constant. Esseen's independent work and later refinements are separate contributions.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.4. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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