docs: add missing usage notes sections and MGF link

[Planeshifter]

Description

What is the purpose of this pull request?

This pull request normalizes three README documentation inconsistencies in the stats/base/dists/beta namespace against the conventions used by the majority of sibling packages. All changes are documentation-only and render no observable output difference.

Namespace summary

• Members analyzed: 15 (cdf, ctor, entropy, kurtosis, logcdf, logpdf, mean, median, mgf, mode, pdf, quantile, skewness, stdev, variance); 0 autogenerated.
• Features analyzed: structural (file tree, package.json key/script sets, README section structure and blockquote-link convention, manifest.json shape, test/benchmark/example naming) and semantic (public signature, return kind, validation prologue in lib/main.js and lib/factory.js, error construction, JSDoc shape, dependencies).
• Features with a clear majority (≥75%): core file set and package.json key set (15/15); validation prologues (consistent by arity — grouped isnan checks for three-argument functions, interleaved for two-argument properties); JSDoc @param/@returns/@example shape; JavaScript-side <section class="notes"> placeholder (12/15); blockquote metric-term reference link (11/14 applicable).
• Features without a clear majority (excluded): the Notes content section (2/15, logcdf/logpdf); secondary test/test.<name>.js naming; the native-binding split (gypfile, C API files — 11/15, excluded as incremental per-package work); language-specific benchmark and fixture files (SciPy/Julia).

cdf

The JavaScript-side usage documentation ran straight from the usage section into the examples section, omitting the empty <section class="notes"> placeholder carried by 12 of 15 (80%) packages in the namespace. This package's own C API section already contains the placeholder, so the JavaScript-side omission is template drift, not intent. Added the placeholder; it renders nothing.

quantile

Same omission — no notes section on the JavaScript side against the 80% namespace majority. Added the empty <section class="notes"> placeholder to match. Documentation output is unchanged.

mgf

The introductory blockquote left "moment-generating function" as plain text while the README body links [moment-generating function][mgf] four times and defines the [mgf] reference. Wrapped the blockquote term in the existing reference link, matching both the in-file usage and the 11 of 14 (79%) applicable siblings that link the metric term in the blockquote.

Related Issues

Does this pull request have any related issues?

No.

Questions

Any questions for reviewers of this pull request?

No.

Other

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

Validation

• Structural extraction (filesystem and string comparison) and semantic extraction (per-package reading of lib/main.js, lib/factory.js, lib/index.js, JSDoc, and READMEs) were run across all 15 members.
• Three-agent drift validation (semantic-review, cross-reference, structural-review) was run on each candidate; all three returned confirmed-drift for the three corrections in this PR. No test or example depends on the edited README content.
• Deliberately excluded: beta/pdf and beta/logpdf blockquote-link fixes (already proposed in open PR chore: propagate recent develop fixes to sibling packages (2026-07-10) #13410); the beta/pdf notes-section placeholder (real drift, but excluded to avoid editing pdf/README.md concurrently with chore: propagate recent develop fixes to sibling packages (2026-07-10) #13410); beta/logcdf (open PR feat: add C implementation for stats/base/dists/beta/logcdf #13649 in flight; not an outlier here regardless); native-binding and language-specific fixture differences (incremental / ecosystem-level, not drift); and all features lacking a clear ≥75% majority.

Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines.

AI Assistance

When authoring the changes proposed in this PR, did you use any kind of AI assistance?

• Yes
• No

If you answered "yes" above, how did you use AI assistance?

• Code generation (e.g., when writing an implementation or fixing a bug)
• Test/benchmark generation
• Documentation (including examples)
• Research and understanding

Disclosure

If you answered "yes" to using AI assistance, please provide a short disclosure indicating how you used AI assistance.

This pull request was authored by Claude Code as an automated cross-package drift-detection run over the stats/base/dists/beta namespace. Candidate corrections were extracted programmatically from structural and semantic feature comparisons, independently validated by parallel reviewer agents (semantic, cross-reference, and structural review), and confined to documentation. A maintainer should audit and promote out of draft.

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@stdlib-js/reviewers

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Generated by Claude Code

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/beta/cdf	$\\color{green}337/337$ $\\color{green}+100.00\\%$	$\\color{green}29/29$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}337/337$ $\\color{green}+100.00\\%$
stats/base/dists/beta/mgf	$\\color{green}409/409$ $\\color{green}+100.00\\%$	$\\color{green}24/24$ $\\color{green}+100.00\\%$	$\\color{green}5/5$ $\\color{green}+100.00\\%$	$\\color{green}409/409$ $\\color{green}+100.00\\%$
stats/base/dists/beta/quantile	$\\color{green}234/234$ $\\color{green}+100.00\\%$	$\\color{green}23/23$ $\\color{green}+100.00\\%$	$\\color{green}3/3$ $\\color{green}+100.00\\%$	$\\color{green}234/234$ $\\color{green}+100.00\\%$

The above coverage report was generated for the changes in this PR.