fix: return ln(sqrt(2/pi)) instead of NaN for x = 0 and k = 1 in stats/base/dists/chi/logpdf

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• fixes stats/base/dists/chi/logpdf (JS, factory, and C) returning NaN at x = 0 when k = 1.

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

pdf( 0.0, 1.0 );
// returns ~0.798 (= sqrt(2/pi), the half-normal density at 0)

logpdf( 0.0, 1.0 );
// returns NaN, expected ~-0.226

The log density is (1-k/2) ln 2 + (k-1) ln(x) - x^2/2 - ln Gamma(k/2). With k = 1 and x = 0, the middle term is 0 * -Infinity = NaN, but x^(k-1) = x^0 is 1 there. The fix skips (k-1) ln(x) when k = 1. For other k, x = 0 still gives +Infinity (k < 1) or -Infinity (k > 1), as it did before. I kept the order of the remaining additions as it was, so every other result is unchanged bit for bit. Rearranging the sum shifts rounding enough to fail 388 of the existing fixture checks.

Related Issues

Does this pull request have any related issues?

No.

Questions

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No.

Other

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

• Added a test for x = 0 with k = 1, k < 1 and k > 1 in test.logpdf.js, test.factory.js and test.native.js. The k = 1 assertion fails on develop, and all tests pass here.
• Found with a sweep comparing every stats/base/dists function against SciPy at the support boundaries. Some other densities also return 0 at x = 0 where the density is finite or infinite: weibull for k <= 1, kumaraswamy for a <= 1, betaprime for alpha <= 1, and log-logistic for beta <= 1. gamma, beta, chisquare and f already handle this case. I'll send those as separate PRs so each can be reviewed on its own.

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• Read, understood, and followed the contributing guidelines.

AI Assistance

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• Yes
• No

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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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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/chi/logpdf	$\\color{green}319/319$ $\\color{green}+100.00\\%$	$\\color{green}33/33$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}319/319$ $\\color{green}+100.00\\%$

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

[kgryte]

@Planeshifter Mind taking a look at this PR?