test: migrate stats/base/dists/beta/pdf to ULP-based assertions

[kgryte]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• migrates the tests for stats/base/dists/beta/pdf from relative tolerance assertions (delta <= tol, where tol = N * EPS * abs( expected[ i ] )) to ULP-based assertions using @stdlib/assert/is-almost-same-value.
• updates test/test.pdf.js, test/test.factory.js, and test/test.native.js. Only test files are changed; no implementation, fixture, or documentation changes are included.

Each ULP bound is the measured minimum which passes over the full fixture set (1000 values per fixture). The minimum was determined by computing ulpDifference( actual, expected ) for every fixture value and taking the maximum; for each bound below, N passes and N-1 fails:

Test file	Fixture	Previous tolerance	ULP bound (measured minimum)
test.pdf.js	both_large.json	180.0 * EPS	245
test.pdf.js	large_alpha.json	150.0 * EPS	153
test.pdf.js	large_beta.json	150.0 * EPS	226
test.factory.js	both_large.json	180.0 * EPS	245
test.factory.js	large_alpha.json	150.0 * EPS	160
test.factory.js	large_beta.json	150.0 * EPS	226
test.native.js	both_large.json	180.0 * EPS	245
test.native.js	large_alpha.json	150.0 * EPS	153
test.native.js	large_beta.json	150.0 * EPS	226

Notes:

• The large_alpha bound is 160 in test.factory.js versus 153 in test.pdf.js. The factory-created function and the main export evaluate the pdf in a different order for the same inputs, yielding a slightly different result for x = 0.5585154674819639, alpha = 15.443236158393903, beta = 9.67752027613441.
• The native add-on was built locally (make install-node-addons NODE_ADDONS_PATTERN="stats/base/dists/beta/pdf") and the C implementation reproduced the JavaScript results exactly, so test.native.js uses the same bounds as test.pdf.js.
• The test suite was run twice at the final bounds, producing identical results (9093 passing assertions, 0 failing) in both runs.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352

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.

• make test TESTS_FILTER=".*/stats/base/dists/beta/pdf/.*" passes (run twice).
• make lint-javascript-tests TESTS_FILTER=".*/stats/base/dists/beta/pdf/.*" is clean.
• EditorConfig linting could not run in the authoring environment because the editorconfig-checker binary download was blocked by a network policy. The changed files were instead checked manually for LF line endings, tab indentation, no new trailing whitespace, and a final newline.

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 helps reviewers determine how much scrutiny to apply when reviewing your contribution. Example disclosures: "This PR was written primarily by Claude Code." or "I consulted ChatGPT to understand the codebase, but the proposed changes were fully authored manually by myself.".

This PR was written by Claude Code running as an unattended scheduled task. The test edits, the ULP minimization, and the verification runs described above were all performed by Claude Code; the migration idiom was mirrored from previously merged conversions in this family (e.g. #15656, stats/base/dists/beta/logpdf).

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@stdlib-js/reviewers

🤖 Generated with Claude Code

https://claude.ai/code/session_01HhsK6pmAqQ5LtJMuHQMo7E

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Generated by Claude Code

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/beta/pdf	$\\color{green}387/387$ $\\color{green}+100.00\\%$	$\\color{green}47/47$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}387/387$ $\\color{green}+100.00\\%$

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