fix: avoid cancellation for large b in stats/base/dists/kumaraswamy/median

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• evaluates stats/base/dists/kumaraswamy/median as pow( -expm1( -ln(2)/b ), 1/a ) instead of pow( 1 - pow( 2, -1/b ), 1/a ) (JS and C).

2^(-1/b) is close to 1 for large b, so 1 - 2^(-1/b) cancels:

var median = require( '@stdlib/stats/base/dists/kumaraswamy/median' );

median( 1.0, 1.0e8 );
// develop: 6.931471729920702e-9
// this PR: 6.931471781576802e-9

median( 1.0, 1.0e15 );
// develop: 6.661338147750939e-16 (4% off)
// this PR: 6.931471805599451e-16

Fixtures and tests:

• runner.jl now evaluates the textbook formula (1 - 2^(-1/b))^(1/a) in 2048-bit BigFloat instead of Distributions.median, which uses the same double-precision expression. Distributions is dropped from REQUIRE, and data.json is regenerated with the same input ranges.

• New large_b.json: b log-spaced over [1, 1e15], with a in [0.5, 5.5].

• Max error in JS and native:

  fixture	develop	this PR
  data	587 ULP	442 ULP
  large_b	~2.8e14 ULP	24 ULP

  The tolerances are set to those values; the old one was 9 ULP against Distributions' double-precision values. What's left on data comes from a as small as ~1e-3. Rounding 1/a (about 1000) is then multiplied by |ln(1 - 2^(-1/b))|. That's conditioning, and develop is worse there too. On develop, 838 of the 2,017 assertions in test.js fail. With this change they all pass.

Related Issues

Does this pull request have any related issues?

None. Companion to #15769 (kumaraswamy/quantile).

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. I found the bug by scanning stats/base/dists for 1 - pow(...).

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Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/kumaraswamy/median	$\\color{green}199/199$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}199/199$ $\\color{green}+100.00\\%$

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