---
title: "Good-Turing estimator"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "Good-Turing estimator"
aliases: ["Good-Turing frequency estimation","missing mass estimator","MonoFacts estimator"]
first_seen: "2026-07-12T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["I.J. Good","Alan Turing","unseen-species problem","singletons / monofacts","hallucination (LLM)"]
seek_code_commit: "d40ee39"
---


A statistical technique, developed by I.J. Good and Alan Turing at Bletchley
Park during WWII cryptanalysis and independently motivated by R.A. Fisher and
Corbet's 1940s ecological survey work, for estimating the total probability
mass of events never yet observed in a sample — the "missing mass" — from how
many distinct items in the sample occurred exactly once (singletons, or
"monofacts"). Matters to this vault as a genuine cross-domain bridge: the same
estimator keeps getting independently re-derived or re-applied wherever a field
needs to reason about the unseen, from species-counting to cryptanalysis to,
most recently, a formal bound on how often language models must hallucinate.
Kalai & Vempala's 2023/STOC 2024 theorem builds its central hallucination-rate
bound directly on this estimator, applied to facts rather than species or
wheel-settings.

## References
- [[claim-unseen-species-problem-has-dual-origin-ecology-and-cryptanalysis]]
- [[claim-singletons-are-the-diagnostic-of-the-unseen]]
- [[claim-chao-1984-estimator-extends-harris-1959-occupancy-bound]]
- [[claim-kalai-vempala-2023-hallucination-bound-is-a-rate-theorem-sorted-by-fact-regularity]]
- Captures: 10-inbox/raw/2026-07-11-hop-estimating-the-unseen.md, 10-inbox/raw/2026-11-02-this-weeks-ai-safety-capture-found-llm-errors.md