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The 37 pages that link to Central limit theorem, each with the reason it gives.

• Monte Carlo methodRelated: It often justifies approximate error bars for averages from sufficiently large samples.

• Sampling distributionRelated: It explains why many sample-mean distributions become approximately normal as sample size grows.

• Normal distributionRelated: It explains why normal approximations arise for sample sums and averages.

• Binomial distributionRelated: It explains why large-count binomial distributions can be approximated by a normal curve.

• Characteristic functionRelated: Characteristic functions provide a standard proof by tracking transforms of normalized sums.

• Law of large numbersCompared with: It describes the shape of fluctuations around the average, while the law describes convergence of the average itself.

• Arithmetic meanRelated: It explains why sample means support many large-sample statistical procedures.

• Asymptotic analysisRelated: Its limiting approximation supports estimates for probabilities and statistical quantities.

• Independence (probability theory)Related: Independence is a standard hypothesis in classical versions of the theorem.

• Independent and identically distributed random variablesRelated: The classical theorem applies to sums of i.i.d. variables with finite variance.

• Moment-generating functionRelated: Transform methods, including moment-generating functions under suitable conditions, can establish convergence to the normal distribution.

• Sampling errorRelated: It often makes the distribution of sample-mean errors approximately normal in large samples.

• Standard errorRelated: It explains why sample means often have approximately normal sampling distributions whose spread can be estimated.

• Convergence in distributionBroader topic: Its conclusion is a canonical distributional limit for sums of random variables.

• 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.

• Gaussian distributionRelated: It explains why Gaussian approximations arise even when individual measurements are not Gaussian.

• Student's t-distributionRelated: It explains why t-based approximations can remain useful beyond normally distributed populations.

• Thermal fluctuationsRelated: It explains why many macroscopic thermal fluctuations are approximately Gaussian.

• Independent random variablesRelated: Independent summands are the classical setting for the theorem’s normal approximation.

• Abraham de MoivreNarrower topic: De Moivre’s binomial approximation is an early special case of this broader phenomenon.

• 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.

• Lévy's continuity theoremRelated: Characteristic functions provide a common proof strategy, with Lévy’s theorem converting their limit into distributional convergence.

• Slutsky's theoremRelated: Slutsky’s result helps turn central-limit approximations into usable statistical limits.

• Law of the iterated logarithmCompared with: It describes distributions at fixed sample sizes; the iterated logarithm law controls almost-sure extremes over time.

• Aleksandr LyapunovRelated: His condition for convergence is one of the classical criteria in the theorem’s development.

• Berry–Esseen theoremNarrower topic: The theorem’s history begins with the need to measure the speed of this convergence.

• De Moivre–Laplace theoremNarrower topic: The theorem is an early, specific instance of this broader convergence principle.

• Erdős–Kac theoremRelated: The theorem obtains a normal limit from prime-divisibility indicators resembling a sum of rare events.

• 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.

• Diffusion and random walksRelated: It explains why many random walks acquire Gaussian displacement distributions.

• Fisher–Tippett–Gnedenko theoremCompared with: It concerns sums rather than maxima, producing a different universal limit family.

• Fluctuations and noiseRelated: It explains why Gaussian fluctuations often emerge from many small contributions.

• Ibragimov–Iosifescu conjectureNarrower topic: This is the convergence the conjecture predicts for normalized sums.

• Law of Truly Large NumbersRelated: It describes the shape of aggregate fluctuations, rather than the chance of any rare occurrence.