betainc

Incomplete beta function.

Installation

npm install @stdlib/math-base-special-betainc

Usage

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

betainc( x, a, b[, regularized[, upper]] )

By default, evaluates the regularized lower 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.

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.

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.

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.

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

If provided a negative b, the function returns NaN.

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

Examples

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

var i;
var x;
var a;
var b;

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

See Also

• @stdlib/math-base/special/beta: beta function.
• @stdlib/math-base/special/betaincinv: inverse incomplete beta function.
• @stdlib/math-base/special/betaln: natural logarithm of the beta function.

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.