percentile concept

Definition	The value below which a given fraction of the rows fall. The fraction at or below a value is nondecreasing in the value. Chapter 11 section 11.3.
Example	Among 100 sorted ratios, the 97.5th over the 2.5th percentile is the rank certificate’s percentile setting.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `percentile`, kind concept.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 11.2.
Assumptions and scope	The value below which a given fraction of the rows fall. The fraction at or below a value is nonnegative, at most one, nondecreasing in the value, one at or above the largest row and zero below the smallest, and an upper percentile over a lower one is at least one. The rank certificate’s percentile setting reads the 97.5 over 2.5 percentile ratio as a robust estimate where the strict setting reads the max over min, and the anti-hub gate reads the fifth percentile of recall.
Prior art	none recorded
Evidence	`turboquant-pro/docs/HUBNESS_PRIMER.md:86-131`, `lean/DataMiningAsObservation/Percentile.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

The value below which a given fraction of the rows fall.

Equation

Book equation 11.2.

\[\begin{gathered} r=\frac{d_{\mathrm{compressed}}}{d_{\mathrm{exact}}},\qquad \kappa_{\text{strict}}=\frac{\max r}{\min r},\qquad \tau\ \ge\ 1-2\hat\mu(\kappa_{\text{strict}}),\qquad \rho_S\ \ge\ 1-3\hat\mu(\kappa_{\text{strict}}), \\ \kappa_{97.5/2.5}=\frac{q_{97.5}(r)}{q_{2.5}(r)}\ \text{ gives the same two expressions as estimates, not floors.} \end{gathered}\]

Conditions

The value below which a given fraction of the rows fall. The fraction at or below a value is nonnegative, at most one, nondecreasing in the value, one at or above the largest row and zero below the smallest, and an upper percentile over a lower one is at least one.
The rank certificate’s percentile setting reads the 97.5 over 2.5 percentile ratio as a robust estimate where the strict setting reads the max over min, and the anti-hub gate reads the fifth percentile of recall.

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

Chapter 11 section 11.3 of Data Mining as Observation, with the percentile setting of the rank certificate in turboquant-pro/turboquant_pro.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 11 section 11.6	anti-hub recall, p05, hub-rank correlation, hub-set overlap, the build gate	`turboquant-pro/docs/HUBNESS_PRIMER.md:86-131`

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Percentile.lean, theorems cdf_nonneg, cdf_le_one, cdf_mono, cdf_of_all, cdf_of_none, ratio_ge_one, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation primer S, chapters 3, 10, 11.

rank certificate; anti-hub recall; skewness; threshold; Robin Hood index.

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

← partial derivativepercentile interval →