fix: return the limiting density at x = 0 in stats/base/dists/log-logistic/pdf

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• makes stats/base/dists/log-logistic/pdf (JS, factory, and C) return the limiting density at x = 0 rather than 0.

var pdf = require( '@stdlib/stats/base/dists/log-logistic/pdf' );

// The standard log-logistic has density 1/(1+x)^2, which is 1 at x = 0:
pdf( 0.0, 1.0, 1.0 );   // 0 (and the README/JSDoc example says `returns 0.0`)

// For beta < 1 the density is unbounded near 0:
pdf( 1.0e-10, 1.0, 0.5 ); // ~5e4
pdf( 0.0, 1.0, 0.5 );     // 0

The density is (beta/alpha) (x/alpha)^(beta-1) / (1 + (x/alpha)^beta)^2. At x = 0 its limit is +Infinity for beta < 1, 1/alpha for beta = 1, and 0 for beta > 1. SciPy's fisk.pdf( 0, c ) returns those values (inf, 1, 0 for c = 0.5, 1, 2 with unit scale).

Changes:

• lib/main.js, lib/factory.js, src/main.c: x < 0 still returns 0, and x = 0 now returns +Infinity, 1/alpha or 0. manifest.json gains @stdlib/constants/float64/pinf.
• The documented example pdf( 0.0, 1.0, 1.0 ) now says 1.0, in lib/main.js, lib/native.js, docs/types/index.d.ts and docs/repl.txt.
• Tests: the "x <= 0 returns 0" tests asserted pdf( 0.0, 1.0, 1.0 ) === 0. That point is removed and they now say x < 0. There is a new x = 0 test with beta below, at and above one in test.pdf.js, test.factory.js and test.native.js.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• fix: return +Infinity at x = 0 for k < 1 in stats/base/dists/weibull/pdf and logpdf #15605
• fix: return the limiting density at x = 0 and x = 1 in stats/base/dists/kumaraswamy/pdf and logpdf #15606
• fix: return the limiting density at x = 0 in stats/base/dists/betaprime/logpdf and pdf #15607

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 primarily by Claude Code. The bug was found by comparing every stats/base/dists function against SciPy on random parameters.

---

@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/log-logistic/pdf	$\\color{green}324/324$ $\\color{green}+100.00\\%$	$\\color{green}37/37$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}324/324$ $\\color{green}+100.00\\%$

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

[kgryte]

@Planeshifter Mind taking a look at this one?