feat: add implementation for stats/base/dists/halfnormal/logpdf

[Om-A-osc]

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Progresses #9416.

Description

This pull request adds and validates the half-normal logpdf implementation, including C, JavaScript, and TypeScript bindings, and corrects documentation examples to match the mathematically correct half-normal distribution. The implementation and reference values are aligned with Julia’s Truncated(Normal(0, σ), 0, Inf) ground-truth model.

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

No.

Other

The numerical reference values were verified against Julia’s Distributions.jl implementation of a half-normal distribution via a truncated normal model. Documentation examples were updated to reflect these correct reference values.

Checklist

• Read, understood, and followed the contributing guidelines.

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

I used AI assistance to verify the mathematical formula for the half-normal log-PDF and to confirm expected numerical values using Julia as a reference.

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@stdlib-js/reviewers

[Planeshifter]

Thanks for your first contribution to stdlib!

[Planeshifter]

For consistency with other stdlib C examples, we should use %lf for double values instead of %0.4f.

Suggested change

	printf( "x: %0.4f, σ: %0.4f, ln(f(x;σ)): %0.4f\n", x, sigma, y );
	printf( "x: %lf, σ: %lf, ln(f(x;σ)): %lf\n", x, sigma, y );

The README.md should be updated accordingly.

[stdlib-bot]

Coverage Report

No coverage information available.

[Om-A-osc]

Hello @Planeshifter, I’ve made the requested changes and addressed the review comments. Please have a look when you have a moment. Thank you!