fix: return +Infinity at x = 0 for k < 1 in stats/base/dists/weibull/pdf and logpdf

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• fixes stats/base/dists/weibull/pdf and stats/base/dists/weibull/logpdf returning 0 and -Infinity at x = 0 when the shape k < 1. The density (k/lambda) (x/lambda)^(k-1) exp(-(x/lambda)^k) grows without bound as x -> 0+ in that case.

var pdf = require( '@stdlib/stats/base/dists/weibull/pdf' );

pdf( 0.0, 0.5, 2.0 );
// JavaScript returns 0 and the native addon returns Infinity

The C implementation of pdf has no special case for x = 0 and evaluates the formula, where pow( 0.0, k-1.0 ) is +Infinity. The JavaScript implementation special-cases x = 0 as k === 1 ? k/lambda : 0, which is only right for k >= 1. So the two backends currently disagree. R (dweibull( 0, 0.5, 2 )), SciPy (weibull_min.pdf( 0, 0.5, scale=2 )) and Julia (pdf( Weibull( 0.5, 2 ), 0 )) all return Inf. Within stdlib, gamma, beta, chisquare and f already return +Infinity for the same boundary case.

Changes:

• pdf/lib/main.js, pdf/lib/factory.js: return PINF at x = 0 for k < 1.
• logpdf/lib/main.js, logpdf/lib/factory.js, logpdf/src/main.c: return PINF at x = 0 for k < 1, where it used to be NINF. The C logpdf had the same special case as the JavaScript.
• Tests: the existing "k not equal to one returns 0" cases (which use k = 2) are renamed to "greater than one", and there is a new k < 1 case in each of the six test files.

The k = 1 (1/lambda) and k > 1 (0) results are unchanged.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• fix: return ln(sqrt(2/pi)) instead of NaN for x = 0 and k = 1 in stats/base/dists/chi/logpdf #15604 (the same class of boundary bug in chi/logpdf).

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.

Not changed here: in pdf/src/main.c, the x == +/-Infinity branch returns ( k == 0.0 ) ? k/lambda : 0.0. The k == 0.0 arm can't be reached, since k <= 0 has already returned NaN, so the branch always returns 0, which is the correct result.

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.

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Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/weibull/logpdf	$\\color{green}316/316$ $\\color{green}+100.00\\%$	$\\color{green}39/39$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}316/316$ $\\color{green}+100.00\\%$
stats/base/dists/weibull/pdf	$\\color{green}318/318$ $\\color{green}+100.00\\%$	$\\color{green}40/40$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}318/318$ $\\color{green}+100.00\\%$

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