Nasty Pinguin Manure

# npm

## @stdlib/math-base-special-betaincinv

0.0.5 • Public • Published

# betaincinv

Inverse of the incomplete beta function.

## Installation

`npm install @stdlib/math-base-special-betaincinv`

## Usage

`var betaincinv = require( '@stdlib/math-base-special-betaincinv' );`

#### betaincinv( p, a, b[, upper] )

Inverts the regularized 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. To invert the upper function instead, set the `upper` argument to `true`.

```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`.

```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`.

```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`.

```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`.

```var y = betaincinv( 0.5, 2.0, -2.0 );
// returns NaN

y = betaincinv( 0.5, 2.0, 0.0 );
// returns NaN```

## Examples

```var randu = require( '@stdlib/random-base-randu' );
var betaincinv = require( '@stdlib/math-base-special-betaincinv' );

var i;
var p;
var a;
var b;

for ( i = 0; i < 100; i++ ) {
p = randu();
a = randu() * 10.0;
b = randu() * 10.0;
console.log( 'p: %d, \t a: %d, \t b: %d, \t f(p,a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), betaincinv( p, a, b ) );
}```

## Notice

This package is part of 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, see the main project repository.

### Install

`npm i @stdlib/math-base-special-betaincinv`

stdlib.io

186

### Version

0.0.5

Apache-2.0 AND BSL-1.0

40.6 kB

9