test: migrate stats/base/dists/bradford/variance to ULP-based assertions

[Planeshifter]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• migrates stats/base/dists/bradford/variance test cases from relative tolerance testing to ULP (units in the last place) difference testing, per the guidance in [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352.
• replaces the delta/tol relative-tolerance idiom in test/test.js and test/test.native.js with @stdlib/assert/is-almost-same-value, tightened to the minimum ULP bound that still passes across the full fixture set:
  • small c fixtures: 856 ULPs (both test.js and test.native.js)
  • large c fixtures: 20 ULPs (both test.js and test.native.js)
• these bounds were determined by computing the exact ULP distance between actual and expected values for every fixture (via @stdlib/number/float64/base/ulp-difference) and confirmed to be the minimum integer bound that passes (one ULP lower fails). The test suite was run twice at the final bound to confirm determinism.

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.

No.

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, which searched the codebase for a package still using the relative-tolerance testing idiom, studied prior-art conversions (e.g. #15294 for the sibling stats/base/dists/bradford/entropy package) and issue #11352, converted test/test.js and test/test.native.js to use isAlmostSameValue, and empirically determined the minimum ULP bounds by computing exact ULP differences against the fixtures (building the package's native add-on locally to verify test.native.js as well).

---

@stdlib-js/reviewers

🤖 Generated with Claude Code

https://claude.ai/code/session_011jtHegiyumowZHcu4H1ofX

---

Generated by Claude Code

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/bradford/variance	$\\color{green}183/183$ $\\color{green}+100.00\\%$	$\\color{green}8/8$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}183/183$ $\\color{green}+100.00\\%$

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