feat: initial implementation of stats/base/dists/halfnormal/cdf

[navyansh007]

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---

Progresses #9416

Description

What is the purpose of this pull request?

This pull request:

• Adds a comprehensive implementation of the cumulative distribution function (CDF) for the half-normal distribution
• Implements @stdlib/stats/base/dists/halfnormal/cdf package with complete functionality including:
  • Main CDF function for evaluating the half-normal CDF at a given value
  • Factory function for creating partially applied CDF functions with fixed parameters
  • Full TypeScript type definitions and tests
  • Comprehensive test suite covering edge cases (NaN, infinity, degenerate distributions)
  • Performance benchmarks for both direct calls and factory-generated functions
  • Examples demonstrating usage
  • REPL documentation
  • Test fixture infrastructure using Julia scripts
• Follows the same structure and quality standards as the normal distribution's CDF package

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• #{{TODO: add related issue number}}

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.

Implementation Notes:

The half-normal distribution CDF is implemented using the error function (erf):

F(x;μ,σ) = erf((x-μ)/(σ√2)) for x ≥ μ
F(x;μ,σ) = 0 for x < μ

where μ is the location parameter and σ is the scale parameter.

Package Structure:

The implementation closely mirrors the structure of @stdlib/stats/base/dists/normal/cdf to ensure consistency across the stdlib codebase:

• lib/main.js - Main CDF implementation
• lib/factory.js - Factory function for partial application
• lib/index.js - Package exports
• test/test.cdf.js - Comprehensive tests for the main function
• test/test.factory.js - Tests for the factory function
• test/test.js - Basic module tests
• examples/index.js - Usage examples
• benchmark/benchmark.js - Performance benchmarks
• docs/types/index.d.ts - TypeScript definitions
• docs/types/test.ts - TypeScript definition tests
• docs/repl.txt - REPL documentation
• test/fixtures/julia/ - Test fixture generation scripts

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 me.".

The tests and documentation were primarily authored by Claude Code, but the research and understanding of the half-normal distribution were done by me, and the CDF function's code implementation was entirely authored and reviewed by me.

---

@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/halfnormal/cdf	$\color{red}228/232$ $\color{green}+0.00%$	$\color{red}23/25$ $\color{green}+0.00%$	$\color{green}3/3$ $\color{green}+0.00%$	$\color{red}228/232$ $\color{green}+0.00%$

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

[kgryte]

Suggested change

	"@stdlib/math/base/assert/is-nan": "^0.2.2",
	"@stdlib/math/base/special/erf": "^0.2.2",
	"@stdlib/math/base/special/sqrt": "^0.2.2",
	"@stdlib/stats/base/dists/degenerate/cdf": "^0.2.2",
	"@stdlib/utils/constant-function": "^0.2.2",
	"@stdlib/utils/define-nonenumerable-read-only-property": "^0.2.2"

[kgryte]

Suggested change

	tape('if provided `x < mu`, the function returns `0`', function test(t) {
	tape( 'if provided `x < mu`, the function returns `0`', function test( t ) {

[kgryte]

Suggested change

	t.ok(del <= 1e-14, 'within tolerance. x: ' + x[i] + '. y: ' + y + '. E: ' + expected[i] + '. Delt: ' + del);
	t.ok(del <= 1e-14, 'within tolerance. x: ' + x[i] + '. y: ' + y + '. E: ' + expected[i] + '. Delt: ' + del);

Use assert/is-almost-same-value with an appropriate maxULPs argument.

[kgryte]

Suggested change

	* // returns 0.9544997361036416
	* // returns ~0.9545

[kgryte]

Suggested change

	// returns 0.9544997361036416
	// returns ~0.9545

[Planeshifter]

Missing space before closing parenthesis. stdlib style requires spaces inside function call parentheses: foo( bar ) not foo(bar).

Suggested change

	y = cdf( x[ i % len ], mu[ i % len ], sigma[ i % len ]);
	y = cdf( x[ i % len ], mu[ i % len ], sigma[ i % len ] );

[Planeshifter]

Inconsistent spacing style throughout test file. stdlib requires spaces inside function call parentheses: cdf( x, y, z ) not cdf(x, y, z). Compare with say @stdlib/stats/base/dists/normal/cdf/test/test.cdf.js for reference.

Suggested change

	var y = cdf(NaN, 0.0, 1.0);
	var y = cdf( NaN, 0.0, 1.0 );

[Planeshifter]

Inconsistent spacing style. stdlib requires spaces inside function call parentheses for tape(), t.ok(), t.strictEqual(), etc. Compare with @stdlib/stats/base/dists/normal/cdf/test/test.cdf.js for reference.

Suggested change

	tape('main export is a function', function test(t) {
	tape( 'main export is a function', function test( t ) {
	t.ok( true, __filename );
	t.strictEqual( typeof cdf, 'function', 'main export is a function' );
	t.end();
	});

[navyansh007]

Hey @kgryte @Planeshifter
I have made all the changes exactly as mentioned in the reviews. I request you to please have a look at it. Feel free to let me know in case some further changes are required.

[Planeshifter]

The examples file uses the older randu() + manual loop pattern. To match the current stdlib style (see reference packages like normal/cdf and rayleigh/cdf), this should use the uniform() + logEachMap() pattern:

Suggested change

	var randu = require( '@stdlib/random/base/randu' );
	var cdf = require( './../lib' );
	var sigma;
	var mu;
	var x;
	var y;
	var i;
	for ( i = 0; i < 10; i++ ) {
	x = randu() * 10.0;
	mu = randu() * 5.0;
	sigma = randu() * 10.0;
	y = cdf( x, mu, sigma );
	console.log( 'x: %d, µ: %d, σ: %d, F(x;µ,σ): %d', x, mu, sigma, y );
	}
	var uniform = require( '@stdlib/random/array/uniform' );
	var logEachMap = require( '@stdlib/console/log-each-map' );
	var cdf = require( './../lib' );
	var opts = {
	'dtype': 'float64'
	};
	var x = uniform( 10, 0.0, 10.0, opts );
	var mu = uniform( 10, 0.0, 5.0, opts );
	var sigma = uniform( 10, 0.0, 10.0, opts );
	logEachMap( 'x: %0.4f, µ: %0.4f, σ: %0.4f, F(x;µ,σ): %0.4f', x, mu, sigma, cdf );

[Planeshifter]

The Examples section uses the older randu() + manual loop pattern. To match the current stdlib style (see reference packages like normal/cdf and rayleigh/cdf), this should use uniform() + logEachMap():

Suggested change

	var randu = require( '@stdlib/random/base/randu' );
	var cdf = require( '@stdlib/stats/base/dists/halfnormal/cdf' );
	var sigma;
	var mu;
	var x;
	var y;
	var i;
	for ( i = 0; i < 10; i++ ) {
	x = randu() * 10.0;
	mu = (randu() * 10.0) - 5.0;
	sigma = randu() * 20.0;
	y = cdf( x, mu, sigma );
	console.log( 'x: %d, µ: %d, σ: %d, F(x;µ,σ): %d', x, mu, sigma, y );
	}
	var uniform = require( '@stdlib/random/array/uniform' );
	var logEachMap = require( '@stdlib/console/log-each-map' );
	var cdf = require( '@stdlib/stats/base/dists/halfnormal/cdf' );
	var opts = {
	'dtype': 'float64'
	};
	var x = uniform( 10, 0.0, 10.0, opts );
	var mu = uniform( 10, 0.0, 5.0, opts );
	var sigma = uniform( 10, 0.0, 10.0, opts );
	logEachMap( 'x: %0.4f, µ: %0.4f, σ: %0.4f, F(x;µ,σ): %0.4f', x, mu, sigma, cdf );

[navyansh007]

Hey @Planeshifter
Thanks a lot for your feedback. I highly appreciate you for providing the exact fix to this one.
I have modified the examples to implement uniform() and logEachMap() in the example files (examples/index.js and README.md). I request you to please have a look, and feel free to let me know in case some further changes are required.