Le Cam's Theorem bounds the total variation distance between the distribution of a sum of independent indicator random variables, each with its own small probability of success, and a Poisson distribution with mean equal to the sum of those probabilities, showing the two distributions are close whenever the individual probabilities are small. Named for Lucien Le Cam, it makes precise and quantifies the classical heuristic that a sum of many rare, roughly independent events is well approximated by a Poisson distribution.
Facts
StatementThe sum of independent Bernoulli variables has approximately a Poisson distribution, with the approximation error bounded in total variation distance. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Le Cam's theorem (Wikipedia)
Sources
1. Le Cam's theorem (Wikipedia)
Statement
the sum has approximately a Poisson distribution and the above inequality bounds the approximation error
References
Le Cam, L. (1960). 'An Approximation Theorem for the Poisson Binomial Distribution'.
In Branch: Probability and Statistics, Lead sentence
In probability theory, Le Cam's theorem, named after Lucien Le Cam, states the following.
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