[harsh-thakkar7]

Description

This pull request:

• fixes stats/base/dists/cosine/mgf to return 1 when t is zero; previously it returned NaN for every parameter combination, because the evaluation divides by st = s*t, producing 0/0 at t = 0;

• the limit as t approaches zero is 1 (sinh(st) ~ st cancels the st factor, and M(0) = E[e^{0*X}] = 1 by definition), and the same change is applied to the C implementation in src/main.c.

Related Issues

This pull request has the following related issues:

• none; found while checking distribution MGFs against their limiting values

Questions

No.

Other

Verification:

• mgf( 0.0, 1.0, 2.0 ) returned NaN before and returns 1 after; mgf( 1e-12, 1.0, 2.0 ) already returned 1.000000000001, confirming continuity;
• mgf.factory( 2.0, 5.0 )( 0.0 ) likewise returns 1;
• all previously documented example values are unchanged (e.g., mgf( 0.5, 0.0, 1.0 ) is still ~1.016, mgf( 2.0, 0.0, 3.0 ) is still ~7.234);
• NaN and s <= 0 handling is unchanged, since the new check runs after input validation.

Checklist

• Read, understood, and followed the contributing guidelines.

AI Assistance

• Yes

• No

• Code generation

• Documentation (including examples)

• Research and understanding

Disclosure

This PR was prepared with Qoder AI assistance under the contributor's direction. All changed code was executed locally to verify the values above.

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/cosine/mgf	$\\color{red}296/300$ $\\color{green}+0.00\\%$	$\\color{red}21/23$ $\\color{green}+0.00\\%$	$\\color{green}4/4$ $\\color{green}+0.00\\%$	$\\color{red}296/300$ $\\color{green}+0.00\\%$

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