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.

Multinomial distribution

Definition

For $k \geq 1$ , $n \in N_{0}$ , and $p = (p_{1}, \dots, p_{k})$ with $p_{j} \geq 0$ and $\sum_{j} p_{j} = 1$ , the Multinomial distribution $Multinomial (n, p)$ is the law on count vectors $y \in N_{0}^{k}$ with $\sum_{j} y_{j} = n$ and masses $P (Y = y) = \frac{n!}{\prod_{j} y_{j}!} \prod_{j} p_{j}^{y_{j}},$ using $0^{0} = 1$ . The masses sum to one by The Multinomial mass function is normalized. For $k = 1$ or $n = 0$ , this law is degenerate at its unique admissible count vector.

Depends on

Used by

Dirichlet-Multinomial conjugate update Theorem

Dependency tree · two levels

24 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., §3.4 (standard reference, not scraped)
Gero Walter, A Technical Note on the Dirichlet-Multinomial Model, 2013 (standard reference, not scraped)