DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Exposure-parameterized Poisson law

Definition

For exposure $e \geq 0$ and rate $λ > 0$ , define $Y \sim Pois (e λ)$ to have the scalar Poisson count law with parameter $e λ$ . Thus for $e > 0$ , $P (Y = y ∣ λ, e) = e^{- e λ} \frac{(e λ)^{y}}{y!}, y \in N_{0},$ with $0^{0} = 1$ ; when $e = 0$ this is the point mass at $y = 0$ . The law is normalized by Normalization, moments, and generating function of the Poisson count law. A zero-exposure positive count has likelihood zero.

Depends on

Used by

Dependency tree · two levels

9 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Gelman et al., Bayesian Data Analysis, 3rd ed., §2.4 (standard reference, not scraped)
Günter Last and Mathew Penrose, Lectures on the Poisson Process, 2017, Chapter 1 (standard reference, not scraped)