Inverse incomplete beta function.
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> Inverse of the [incomplete beta function][incomplete-beta-function].
``bash`
npm install @stdlib/math-base-special-betaincinv
`javascript`
var betaincinv = require( '@stdlib/math-base-special-betaincinv' );
#### betaincinv( p, a, b\[, upper] )
Inverts the regularized [incomplete beta function][incomplete-beta-function]. Contrary to the more commonly used definition, in this implementation the first parameter is the probability p and the second and third parameter are a and b. By default, the function inverts the _lower_ regularized [incomplete beta function][incomplete-beta-function]. To invert the _upper_ function instead, set the upper argument to true.
`javascript
var y = betaincinv( 0.2, 3.0, 3.0 );
// returns ~0.327
y = betaincinv( 0.4, 3.0, 3.0 );
// returns ~0.446
y = betaincinv( 0.4, 3.0, 3.0, true );
// returns ~0.554
y = betaincinv( 0.4, 1.0, 6.0 );
// returns ~0.082
y = betaincinv( 0.8, 1.0, 6.0 );
// returns ~0.235
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = betaincinv( NaN, 1.0, 1.0 );
// returns NaN
y = betaincinv( 0.5, NaN, 1.0 );
// returns NaN
y = betaincinv( 0.5, 1.0, NaN );
// returns NaN
`
If provided a value outside [0,1] for p, the function returns NaN.
`javascript
var y = betaincinv( 1.2, 1.0, 1.0 );
// returns NaN
y = betaincinv( -0.5, 1.0, 1.0 );
// returns NaN
`
If provided a nonpositive a, the function returns NaN.
`javascript
var y = betaincinv( 0.5, -2.0, 2.0 );
// returns NaN
y = betaincinv( 0.5, 0.0, 2.0 );
// returns NaN
`
If provided a nonpositive b, the function returns NaN.
`javascript
var y = betaincinv( 0.5, 2.0, -2.0 );
// returns NaN
y = betaincinv( 0.5, 2.0, 0.0 );
// returns NaN
`
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var betaincinv = require( '@stdlib/math-base-special-betaincinv' );
var opts = {
'dtype': 'float64'
};
var p = 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( 'p: %0.4f, \t a: %0.4f, \t b: %0.4f, \t f(p,a,b): %0.4f', p, a, b, betaincinv );
`
*
- [@stdlib/math-base/special/beta][@stdlib/math/base/special/beta]: beta function.
- [@stdlib/math-base/special/betainc][@stdlib/math/base/special/betainc]: 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].
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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
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[deno-url]: https://github.com/stdlib-js/math-base-special-betaincinv/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-betaincinv/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-betaincinv/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-betaincinv/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-betaincinv/tree/esm
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[branches-url]: https://github.com/stdlib-js/math-base-special-betaincinv/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-betaincinv/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/betainc]: https://www.npmjs.com/package/@stdlib/math-base-special-betainc
[@stdlib/math/base/special/betaln]: https://www.npmjs.com/package/@stdlib/math-base-special-betaln