KnowraCentral limit theoremLinked fromLinked fromThe 37 pages that link to Central limit theorem, each with the reason it gives.All 37Broader topic 1Related 23Narrower topic 4Compared with 9Law of large numbersCompared with: It describes the shape of fluctuations around the average, while the law describes convergence of the average itself.Strong law of large numbersCompared with: It describes the fluctuations around the average's limit rather than convergence to that limit alone.Cauchy distributionCompared with: Cauchy samples evade the standard theorem because their variance is infinite and their sums remain Cauchy.Large deviation theoryCompared with: It captures common fluctuations, unlike the exponential-scale tails studied here.Paul LévyCompared with: Lévy’s stable-law limit theory extends the Gaussian outcome to heavy-tailed variables.Law of the iterated logarithmCompared with: It describes distributions at fixed sample sizes; the iterated logarithm law controls almost-sure extremes over time.Glivenko–Cantelli theoremCompared with: It gives a distributional approximation for fluctuations rather than almost-sure uniform convergence.Cramér's decomposition theoremCompared with: The central limit theorem builds approximate normality from summands; Cramér's theorem reverses the implication exactly.Fisher–Tippett–Gnedenko theoremCompared with: It concerns sums rather than maxima, producing a different universal limit family.