The empirical distribution function built from a sample of independent, identically distributed random variables converges uniformly, with probability one, to the true underlying distribution function as the sample size grows. Named for Valery Glivenko and Francesco Paolo Cantelli, it is sometimes called the fundamental theorem of statistics.
Facts
StatementThe theorem shows that the empirical distribution function built from independent identically distributed samples converges uniformly, almost surely, to the true underlying cumulative distribution function as the sample size grows, which is why it is sometimes called the fundamental theorem of statistics. 1 Proof YearProved by Valery Glivenko and Francesco Cantelli in 1933. Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Proved By
Source Glivenko-Cantelli Theorem (Wikipedia)
Sources
1. Glivenko-Cantelli Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, first sentence
In the theory of probability, the Glivenko-Cantelli theorem (sometimes referred to as the fundamental theorem of statistics), named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli, describes the asymptotic behaviour of the empirical distribution function as the number of independent and identically distributed observations grows.
body text, attribution sentence
This theorem originates with Valery Glivenko and Francesco Cantelli, in 1933.
Proved By: Francesco Paolo Cantelli, Lead section
named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli
In Group: Probability Theory, Lead section
In the theory of probability, the Glivenko-Cantelli theorem (sometimes referred
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