Central Limit Theorem (modern form)
GPTKB entity
Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
statistical theorem
|
| gptkbp:appliesTo |
random variables with finite mean and variance
|
| gptkbp:category |
statistical analysis
probability theorems |
| gptkbp:describes |
distribution of sum of independent random variables
|
| gptkbp:form |
(X₁ + X₂ + ... + Xₙ - nμ)/(σ√n) → N(0,1) as n → ∞
|
| gptkbp:formedBy |
early 20th century
|
| gptkbp:generalizes |
gptkb:Berry–Esseen_theorem
gptkb:Lindeberg–Feller_theorem Lyapunov central limit theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Central Limit Theorem (modern form)
|
| gptkbp:implies |
sample mean approximates normal distribution as sample size increases
|
| gptkbp:provenBy |
gptkb:Pierre-Simon_Laplace
gptkb:Jarl_Waldemar_Lindeberg gptkb:Aleksandr_Lyapunov gptkb:Andrey_Kolmogorov |
| gptkbp:relatedTo |
gptkb:normal_distribution
gptkb:law_of_large_numbers |
| gptkbp:requires |
finite variance
identical distribution (in classical form) independence of random variables |
| gptkbp:state |
sum of large number of independent, identically distributed random variables tends toward normal distribution
|
| gptkbp:usedIn |
gptkb:machine_learning
gptkb:probability_theory data science statistics |
| gptkbp:bfsParent |
gptkb:Central_Limit_Theorem_(early_form)
|
| gptkbp:bfsLayer |
7
|