Incomplete beta function.
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> [Incomplete beta function][incomplete-beta-function].
``bash`
npm install @stdlib/math-base-special-betainc
`javascript`
var betainc = require( '@stdlib/math-base-special-betainc' );
#### betainc( x, a, b\[, regularized\[, upper]] )
By default, evaluates the regularized lower [incomplete beta function][incomplete-beta-function] for inputs x, a > 0 and b > 0. The fourth and fifth parameters of the function can be used to specify whether instead to evaluate the non-regularized and/or upper incomplete beta functions, respectively.
`javascript
var y = betainc( 0.5, 2.0, 2.0 );
// returns 0.5
y = betainc( 0.5, 2.0, 2.0, false );
// returns ~0.083
y = betainc( 0.2, 1.0, 2.0 );
// returns 0.36
y = betainc( 0.2, 1.0, 2.0, true, true );
// returns 0.64
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = betainc( NaN, 1.0, 1.0 );
// returns NaN
y = betainc( 0.8, NaN, 1.0 );
// returns NaN
y = betainc( 0.8, 1.0, NaN );
// returns NaN
`
If provided a x outside the interval [0,1], the function returns NaN.
`javascript
var y = betainc( 1.5, 1.0, 1.0 );
// returns NaN
y = betainc( -0.5, 1.0, 1.0 );
// returns NaN
`
If provided a negative a, the function returns NaN.
`javascript`
var y = betainc( 0.5, -2.0, 2.0 );
// returns NaN
If provided a negative b, the function returns NaN.
`javascript`
var y = betainc( 0.5, 2.0, -2.0 );
// returns NaN
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var betainc = require( '@stdlib/math-base-special-betainc' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 100, 0.0, 1.0, opts );
var a = uniform( 100, 0.0, 10.0, opts );
var b = uniform( 100, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, \t a: %0.4f, \t b: %0.4f, \t f(x,a,b): %0.4f', x, a, b, betainc );
`
*
- [@stdlib/math-base/special/beta][@stdlib/math/base/special/beta]: beta function.
- [@stdlib/math-base/special/betaincinv][@stdlib/math/base/special/betaincinv]: inverse incomplete beta function.
- [@stdlib/math-base/special/betaln][@stdlib/math/base/special/betaln]: natural logarithm of the beta function.
*
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
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---
See [LICENSE][stdlib-license].
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[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-betainc/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-betainc/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-betainc/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-betainc/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-betainc/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-betainc/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-betainc/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-betainc/main/LICENSE
[incomplete-beta-function]: https://en.wikipedia.org/wiki/Incomplete_beta_function
[@stdlib/math/base/special/beta]: https://www.npmjs.com/package/@stdlib/math-base-special-beta
[@stdlib/math/base/special/betaincinv]: https://www.npmjs.com/package/@stdlib/math-base-special-betaincinv
[@stdlib/math/base/special/betaln]: https://www.npmjs.com/package/@stdlib/math-base-special-betaln