Kernel Betainc

Incomplete beta function and its first derivative.

Usage

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

kernelBetainc( [out,] x, a, b, regularized, upper )

The function 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( 2.0, 2.0, false, false );
// returns [ ~0.083, ~1.5 ]

out = kernelBetainc( 0.2, 1.0, 2.0, true, false );
// returns [ 0.32, 1.6 ]

out = kernelBetainc( 0.2, 1.0, 2.0, true, true );
// returns [ 0.64, 1.6 ]

By default, the function returns the incomplete beta function and its first derivative as a two-element array. To avoid extra memory allocation, the function supports providing an output (destination) object.

var Float64Array = require( '@stdlib/array/float64' );

var out = new Float64Array( 2 );

var v = kernelBetainc( out, 0.2, 1.0, 2.0, true, true );
// returns <Float64Array>[ 0.64, 1.6 ]

var bool = ( v === out );
// returns true

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 ]

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 = new Array( 2 );
for ( i = 0; i < 100; i++ ) {
    x = randu();
    a = randu() * 10.0;
    b = randu() * 10.0;
    out = kernelBetainc( out, x, a, b, true, false );
    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 ) );
}