Kernel Betainc

Incomplete beta function and its first derivative.

Installation

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

Usage

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

kernelBetainc( x, a, b, regularized, upper )

Evaluates the 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.

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 ].

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 ].

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 ].

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 and its first derivative for parameters x, a > 0 and b > 0 and assigns results to a provided output array.

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 <Float64Array>[ 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

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( 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: incomplete 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.

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Copyright

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