feat: add C implementation for stats/base/dists/erlang/pdf

[rautelaKamal]

Ref #3575.

Description

What is the purpose of this pull request?

This pull request:

• Adds a C implementation for @stdlib/stats/base/dists/erlang/pdf, fulfilling the open RFC [RFC]: Add C implementation for @stdlib/stats/base/dists/erlang/pdf #3575.
• Validates that the shape parameter k is a non-negative integer using stdlib_base_is_nonnegative_integer(k).
• Reuses the existing Gamma distribution implementation by safely proxying the evaluation directly to the stdlib_base_dists_gamma_pdf C function, since the Erlang distribution is mathematically a special case of the Gamma distribution.
• Integrates standard N-API bindings, Makefile, include.gypi, binding.gyp, and the native.js benchmarks & tests.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• [RFC]: Add C implementation for @stdlib/stats/base/dists/erlang/pdf #3575

Questions

Any questions for reviewers of this pull request?

No.

Other

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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.".

I utilized an AI coding assistant to help scaffold the C implementations, N-API bindings, makefiles, and native benchmarks. The logic was reviewed and verified manually to ensure mathematical correctness and alignment with standard project practices.

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@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
blas/ext/base	$\color{red}59225/70981$ $\color{green}+83.44%$	$\color{red}1066/1209$ $\color{green}+88.17%$	$\color{red}20/601$ $\color{green}+3.33%$	$\color{red}59225/70981$ $\color{green}+83.44%$
blas/ext/base/ndarray	$\color{red}8859/9468$ $\color{green}+93.57%$	$\color{red}153/155$ $\color{green}+98.71%$	$\color{red}0/77$ $\color{green}+0.00%$	$\color{red}8859/9468$ $\color{green}+93.57%$
stats/base/dists/erlang/pdf	$\color{green}289/289$ $\color{green}+0.00%$	$\color{green}11/11$ $\color{green}+0.00%$	$\color{green}3/3$ $\color{green}+0.00%$	$\color{green}289/289$ $\color{green}+0.00%$

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

[Om-A-osc]

@rautelaKamal
CI checks failing for package.json.
Order of keys is important for package.json linting. Maybe have a look at lib/node_modules/@stdlib/stats/base/dists/erlang/mean/package.json and try rearranging.

[Planeshifter]

This file needs to mirror test/test.pdf.js. Currently missing:

• fixture-based tests against ./fixtures/julia/large_rate.json, large_shape.json, both_large.json
• tests for +infinity / -infinity for x
• tests for the degenerate distribution when k == 0
• missing imports (abs, PINF, NINF, EPS)
• missing // FIXTURES // section

See test/test.pdf.js in this same package and @stdlib/stats/base/dists/erlang/mgf/test/test.native.js for the expected structure.

[Planeshifter]

Don't manually populate dependencies. These are auto-generated. Should be:

Suggested change

	"dependencies": {
	"@stdlib/math/base/assert/is-nonnegative-integer": "^0.2.2",
	"@stdlib/stats/base/dists/gamma/pdf": "^0.2.2"
	},
	"dependencies": {},

[Planeshifter]

Missing benchmark/c/ directory (benchmark.c and Makefile) and examples/c/ directory (example.c and Makefile). These are required when adding a C implementation. See, e.g., @stdlib/stats/base/dists/erlang/mgf for reference.

[Planeshifter]

The README.md needs a C APIs section documenting the C interface (usage, examples, function signature). See @stdlib/stats/base/dists/erlang/mgf/README.md for the expected structure.

[rautelaKamal]

Thank you for the detailed feedback. I've addressed all the review comments: mirrored the fixture/infinity/degenerate k=0 tests into test.native.js, added benchmark/c/ and examples/c/ directories with Makefiles, and added the C APIs section to the README