feat: add stats/base/dists/halfnormal/pdf

[Om-A-osc]

Progresses #9416.

Description

This pull request:

• Adds the probability density function (PDF) implementation for the half-normal distribution.
• Includes JavaScript and native implementations, along with tests, benchmarks, examples, and Julia fixtures for validation.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• [RFC]: Tracking issue for complete implementation of @stdlib/stats/base/dists/halfnormal package #9416

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.

I used AI assistance to verify the mathematical formula for the half-normal PDF and to confirm expected numerical values.

---

@stdlib-js/reviewers

[stdlib-bot]

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/halfnormal/pdf	$\color{green}279/279$ $\color{green}+0.00%$	$\color{green}21/21$ $\color{green}+0.00%$	$\color{green}4/4$ $\color{green}+0.00%$	$\color{green}279/279$ $\color{green}+0.00%$

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

[Planeshifter]

Thanks for opening your first PR!

Please address the review comments and workflow failures.

[Planeshifter]

This PR should be getting close; left one more round of comments.

[Om-A-osc]

Hello @Planeshifter, I’ve updated the PR with the changes you requested and addressed the new comments. Could you please take another look when you have time? Let me know if everything looks good to proceed with merging. Thank you!

[Planeshifter]

Did another pass.

[Om-A-osc]

@Planeshifter Thank you for carefully reviewing my changes. This is my first time contributing to stdlib, and I really appreciate you taking the time to point out and help me correct my mistakes. I’ve addressed your previous comments and made the requested changes please have another look and let me know if everything looks good now.

[Planeshifter]

Left another round of comments.

[Om-A-osc]

@Planeshifter did the changes.