The Lindeberg universality principle is a comparison method showing that expectations of sufficiently smooth functions of sums of independent random variables are governed mainly by the means and variances of the summands rather than by finer details of their statistical distributions (Tropp 2023, pp. 275-276). The proof replaces the summands one at a time and bounds each change using Taylor's theorem. Comparing general summands with ones having a normal distribution gives a route to the central limit theorem.
Lindeberg Universality Principle
See also
Central Limit Theorem, Lindeberg Condition, Lindeberg-Feller Central Limit Theorem, Normal Distribution, UniversalityExplore with Wolfram|Alpha
References
Lindeberg, J. W. "Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung." Math. Z. 15, 211-225, 1922.Tropp, J. A. Probability Theory & Computational Mathematics. Caltech CMS Lecture Notes 2023-01. Pasadena, CA: California Institute of Technology, pp. 275-276, 2023. https://doi.org/10.7907/q75sz-e1e79.Cite this as:
Weisstein, Eric W. "Lindeberg Universality Principle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LindebergUniversalityPrinciple.html