docs: fix parameter descriptions and update spacing

[Planeshifter]

Description

> What is the purpose of this pull request?

Propagating fixes merged to develop between 2026-07-26 00:12 PDT (0239983) and 2026-07-26 03:02 PDT (a7865fd) to sibling packages carrying the same defect.

Pattern: rate parameter → scale parameter (invgamma)

Commit b06219c (#13653) corrected a test description in invgamma/quantile, relabeling beta from "rate parameter" to "scale parameter" — for X ~ Gamma(α, β), 1/X ~ InvGamma(α, β) with β a scale, not rate, consistent with stdlib's moment formulas (e.g., mean = β/(α−1)) and the Julia Distributions.jl fixture generators (InverseGamma(alpha, beta), θ = scale). This propagates the fix to the 101 remaining "rate parameter" occurrences across 64 files under stats/base/dists/invgamma/** — JSDoc/TSDoc and C doxygen @param blocks, README prose and C-API bullets, docs/repl.txt, test descriptions, example comments, and Julia fixture-runner docstrings — several files had both correct and stale labels side by side. Variable names (largeRate) and fixture filenames (large_rate.json) are left as-is, matching the source commit.

• b06219c (chore: clean-up)
  • stats/base/dists/invgamma/{cdf,ctor,entropy,kurtosis,logpdf,mean,mode,pdf,quantile,skewness,stdev,variance}
  • stats/base/dists/invgamma/docs/types/index.d.ts (namespace declarations)

Pattern: doxygen one-liner expansion (invgamma siblings)

PR #13653 (b06219c7a) expanded the doxygen one-liner in quantile's header and src/main.c from "Evaluates the quantile function for an inverse gamma distribution." to name alpha, beta, and the evaluation argument explicitly; logpdf already carried the expanded form in its header. pdf and cdf still had the short form in their headers while their own src/main.c already had the expanded sentence — this propagates that same expansion into pdf/include/.../pdf.h and cdf/include/.../cdf.h, copied byte-for-byte from each package's src/main.c. Headers and implementation now agree across all four invgamma packages.

• b06219c (chore: clean-up)
  • stats/base/dists/invgamma/pdf (header only)
  • stats/base/dists/invgamma/cdf (header only)

Pattern: unspaced index brackets and paren spacing in dists test suites

Follows up on b06219c (#13653) by completing the bracket/paren spacing sweep across the remaining stats/base/dists/anglit and stats/base/dists/invgamma test files: 304 lines across 46 files normalize x[i] → x[ i ] style index accesses (expected, alpha, beta, sigma, mu, p, values), plus one unspaced outer-paren t.strictEqual call in anglit/cdf/test/test.factory.js. Purely mechanical spacing changes to match stdlib style; no logic, variable names, or test messages touched.

• b06219c (chore: clean-up)
  • stats/base/dists/anglit/{cdf,entropy,mean,median,mode,quantile,skewness,stdev,variance} test files
  • stats/base/dists/invgamma/{cdf,ctor,entropy,kurtosis,logpdf,mean,mode,pdf,quantile,skewness,stdev,variance} test files

Pattern: @param whitespace propagation from #13654

01a20c0 (#13654) removed doubled spaces around the - separator in @param tags but only covered random/iter/* and stats/base/dists/binomial/quantile. A repo-wide sweep for the same defect turned up one more site: blas/base/gscal/lib/main.js, where stride - stride length collapses to a single space. The other four hits are out of scope — random/strided/docs/types/index.d.ts is generated, random/strided/weibull/docs/types/index.d.ts and ml/incr/sgd-regression/lib/validate.js are superseded by open PRs #12571 and #13641, and the _tools transformer hit is a doubled-hyphen defect requiring a different fix.

• 01a20c0 (style: remove extraneous whitespace)
  • blas/base/gscal

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

• Search scope. Per source pattern: rg 'rate parameter' over stats/base/dists/invgamma/** (101 hits, 64 files; zero hits under random/** invgamma packages, which already say "scale"); rg for short-form doxygen descriptions over invgamma headers and sources; rg '\[[a-z0-9]+\]' over stats/base/dists/{anglit,invgamma}/**/test/*.js (304 hits, 46 files; anglit/pdf and invgamma/quantile/test/test.native.js correctly absent — already fixed by the source commit); repo-wide sweep for doubled-space @param separators (5 hits, 4 excluded).
• Two independent Opus validation agents each read every candidate file in full and confirmed the defect at all sites, including independently deriving that invgamma's beta is a scale parameter (pdf form, scale-linear moment formulas, Distributions.jl parameterization) and verifying the namespace docs/types/index.d.ts is hand-maintained, not generated. An adaptation pass produced byte-exact patches (confirming C doxygen @param column alignment is preserved and no markdown link labels or `[in]` code spans are touched), and a style-consistency pass verified the post-fix text against already-correct siblings (rayleigh, f dist test descriptions; random/base/invgamma docs).
• Zero sites were rejected or rated needs-human; every changed line was audited against the expected transformation shapes after application (407 changed lines = 101 + 304 + 2 headers, with the paren fix landing on an already-counted line).

Deliberately excluded:

• Sites in open-PR collision or generated files (see the @param pattern above).
• test: ULP-migration commits (d98aba7, 4588717) — tracked campaign work ([RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352), not propagatable defect fixes.
• docs: update related packages sections (0239983) — auto-generated churn.
• Two zero-site patterns from b06219c: "modified huber" → "modified Huber" capitalization (only intentional lowercase npm keywords remain) and README NaN per-argument example coverage (all ml/base/loss siblings already correct).
• largeRate variables and large_rate.json fixture filenames (renaming would cascade into fixture regeneration; matches source-commit precedent).
• Adjacent pre-existing defects observed but out of pattern scope: garbled clause in invgamma/entropy/README.md, doubled space in invgamma/pdf/README.md link prose, missing C++ name-mangling comment in cdf.h, and the _tools doubled-hyphen @param defect — logged for a future maintenance pass.

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

This PR was authored by Claude Code on behalf of @Planeshifter as an automated propagation of fixes merged to develop over the prior 24 hours. Candidate source commits were filtered for generalizable patterns, sibling sites located via grep-able pattern signatures, and each proposed patch independently validated by parallel reviewer agents (two Opus validation passes, an adaptation pass, and a style-consistency pass) before commits were applied. A maintainer should audit and promote out of draft.

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Generated by Claude Code

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
blas/base/gscal	$\\color{green}314/314$ $\\color{green}+100.00\\%$	$\\color{green}34/34$ $\\color{green}+100.00\\%$	$\\color{green}3/3$ $\\color{green}+100.00\\%$	$\\color{green}314/314$ $\\color{green}+100.00\\%$
stats/base/dists/anglit/cdf	$\\color{green}327/327$ $\\color{green}+100.00\\%$	$\\color{green}27/27$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}327/327$ $\\color{green}+100.00\\%$
stats/base/dists/anglit/entropy	$\\color{green}194/194$ $\\color{green}+100.00\\%$	$\\color{green}9/9$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}194/194$ $\\color{green}+100.00\\%$
stats/base/dists/anglit/mean	$\\color{green}175/175$ $\\color{green}+100.00\\%$	$\\color{green}9/9$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}175/175$ $\\color{green}+100.00\\%$
stats/base/dists/anglit/median	$\\color{green}175/175$ $\\color{green}+100.00\\%$	$\\color{green}9/9$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}175/175$ $\\color{green}+100.00\\%$
stats/base/dists/anglit/mode	$\\color{green}175/175$ $\\color{green}+100.00\\%$	$\\color{green}9/9$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}175/175$ $\\color{green}+100.00\\%$
stats/base/dists/anglit/quantile	$\\color{green}297/297$ $\\color{green}+100.00\\%$	$\\color{green}27/27$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}297/297$ $\\color{green}+100.00\\%$
stats/base/dists/anglit/skewness	$\\color{green}175/175$ $\\color{green}+100.00\\%$	$\\color{green}9/9$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}175/175$ $\\color{green}+100.00\\%$
stats/base/dists/anglit/stdev	$\\color{green}180/180$ $\\color{green}+100.00\\%$	$\\color{green}9/9$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}180/180$ $\\color{green}+100.00\\%$
stats/base/dists/anglit/variance	$\\color{green}181/181$ $\\color{green}+100.00\\%$	$\\color{green}9/9$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}181/181$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/cdf	$\\color{green}299/299$ $\\color{green}+100.00\\%$	$\\color{green}25/25$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}299/299$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/ctor	$\\color{green}408/408$ $\\color{green}+100.00\\%$	$\\color{green}31/31$ $\\color{green}+100.00\\%$	$\\color{green}16/16$ $\\color{green}+100.00\\%$	$\\color{green}408/408$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma	$\\color{red}2014/2363$ $\\color{green}+85.23\\%$	$\\color{green}29/29$ $\\color{green}+100.00\\%$	$\\color{red}0/27$ $\\color{green}+0.00\\%$	$\\color{red}2014/2363$ $\\color{green}+85.23\\%$
stats/base/dists/invgamma/entropy	$\\color{green}201/201$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}201/201$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/kurtosis	$\\color{green}203/203$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}203/203$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/logpdf	$\\color{green}313/313$ $\\color{green}+100.00\\%$	$\\color{green}25/25$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}313/313$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/mean	$\\color{green}192/192$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}192/192$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/mode	$\\color{green}195/195$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}195/195$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/pdf	$\\color{green}313/313$ $\\color{green}+100.00\\%$	$\\color{green}25/25$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}313/313$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/quantile	$\\color{green}307/307$ $\\color{green}+100.00\\%$	$\\color{green}24/24$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}307/307$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/skewness	$\\color{green}193/193$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}193/193$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/stdev	$\\color{green}196/196$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}196/196$ $\\color{green}+100.00\\%$
stats/base/dists/invgamma/variance	$\\color{green}196/196$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}196/196$ $\\color{green}+100.00\\%$

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