https://github.com/stdlib-js/math-base-special-kernel-betainc
Incomplete beta function and its first derivative.
https://github.com/stdlib-js/math-base-special-kernel-betainc
approximation beta derivative function incomplete-beta javascript kernel math mathematics node node-js nodejs number scalar special special-function stdlib
Last synced: 3 months ago
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Incomplete beta function and its first derivative.
- Host: GitHub
- URL: https://github.com/stdlib-js/math-base-special-kernel-betainc
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:41:11.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2025-06-27T17:26:02.000Z (8 months ago)
- Last Synced: 2025-09-05T02:46:41.254Z (5 months ago)
- Topics: approximation, beta, derivative, function, incomplete-beta, javascript, kernel, math, mathematics, node, node-js, nodejs, number, scalar, special, special-function, stdlib
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 2.61 MB
- Stars: 2
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
- Notice: NOTICE
Awesome Lists containing this project
README
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# Kernel Betainc
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> [Incomplete beta function][incomplete-beta-function] and its first derivative.
## Installation
```bash
npm install @stdlib/math-base-special-kernel-betainc
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var kernelBetainc = require( '@stdlib/math-base-special-kernel-betainc' );
```
#### kernelBetainc( x, a, b, regularized, upper )
Evaluates the [incomplete beta function][incomplete-beta-function] and its first derivative for parameters `x`, `a > 0` and `b > 0`. The `regularized` and `upper` boolean parameters are used to specify whether to evaluate the regularized or non-regularized and the upper or lower incomplete beta functions, respectively.
```javascript
var out = kernelBetainc( 0.8, 1.0, 0.3, false, false );
// returns [ ~1.277, ~0.926 ]
out = kernelBetainc( 0.2, 1.0, 2.0, true, false );
// returns [ 0.36, 1.6 ]
out = kernelBetainc( 0.2, 1.0, 2.0, true, true );
// returns [ 0.64, 1.6 ]
```
If provided `NaN` for `x`, `a`, or `b`, the function returns `[ NaN, NaN ]`.
```javascript
var out = kernelBetainc( NaN, 1.0, 1.0, true, true );
// returns [ NaN, NaN ]
out = kernelBetainc( 0.8, NaN, 1.0, true, true );
// returns [ NaN, NaN ]
out = kernelBetainc( 0.8, 1.0, NaN, true, true );
// returns [ NaN, NaN ]
```
If `x` is outside the interval `[0,1]`, the function returns `[ NaN, NaN ]`.
```javascript
var out = kernelBetainc( 1.5, 1.0, 1.0, true, true );
// returns [ NaN, NaN ]
out = kernelBetainc( -0.5, 1.0, 1.0, true, true );
// returns [ NaN, NaN ]
```
If `a` or `b` is negative, the function returns `[ NaN, NaN ]`.
```javascript
var out = kernelBetainc( 0.5, -2.0, 2.0, true, true );
// returns [ NaN, NaN ]
out = kernelBetainc( 0.5, 2.0, -2.0, true, true );
// returns [ NaN, NaN ]
```
#### kernelBetainc.assign( x, a, b, regularized, upper, out, stride, offset )
Evaluates the [incomplete beta function][incomplete-beta-function] and its first derivative for parameters `x`, `a > 0` and `b > 0` and assigns results to a provided output array.
```javascript
var Float64Array = require( '@stdlib/array-float64' );
var out = new Float64Array( 2 );
var v = kernelBetainc.assign( 0.2, 1.0, 2.0, true, true, out, 1, 0 );
// returns [ 0.64, 1.6 ]
var bool = ( v === out );
// returns true
```
The `offset` parameter specifies the index of the first output array element, and the `stride` parameter specifies the stride length between consecutive output array elements.
## Examples
```javascript
var randu = require( '@stdlib/random-base-randu' );
var kernelBetainc = require( '@stdlib/math-base-special-kernel-betainc' );
var out;
var i;
var x;
var a;
var b;
out = [ 0.0, 0.0 ];
for ( i = 0; i < 100; i++ ) {
x = randu();
a = randu() * 10.0;
b = randu() * 10.0;
kernelBetainc.assign( x, a, b, true, false, out, 1, 0 );
console.log( 'x: %d, \t a: %d, \t b: %d, \t f(x,a,b): %d, \t f^1(x,a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), out[ 0 ].toFixed( 4 ), out[ 1 ].toFixed( 4 ) );
}
```
* * *
## See Also
- [`@stdlib/math-base/special/betainc`][@stdlib/math/base/special/betainc]: incomplete beta function.
* * *
## Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
## Copyright
Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-kernel-betainc.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-kernel-betainc
[test-image]: https://github.com/stdlib-js/math-base-special-kernel-betainc/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-kernel-betainc/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-kernel-betainc?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-kernel-betainc/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-kernel-betainc/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-kernel-betainc/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/blob/main/branches.md
[incomplete-beta-function]: https://en.wikipedia.org/wiki/Incomplete_beta_function
[@stdlib/math/base/special/betainc]: https://github.com/stdlib-js/math-base-special-betainc