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

[DivyanshuVortex]

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/mean from relative tolerance testing to ULP difference testing, per [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352.
• replaces the legacy y === expected[i] / delta <= tol branch in the fixture loops of the test files with t.strictEqual( isAlmostSameValue( y, expected[ i ], N ), true, 'returns expected value' );.
• adds the @stdlib/assert/is-almost-same-value require and drops any unused abs and EPS requires.

These bounds were determined empirically using a script that calculated the maximum ULP difference across all fixture combinations.

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.

Test results via make test TESTS_FILTER=".*/stats/base/dists/beta/mean/.*" passed cleanly.

Checklist

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

• Read, understood, and followed the contributing guidelines.

AI Assistance

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• Yes
• No

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

Disclosure

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@stdlib-js/reviewers

[stdlib-bot]

Hello! 👋

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/beta/mean	$\\color{green}195/195$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}195/195$ $\\color{green}+100.00\\%$

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