betainc

Incomplete beta function.

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 uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var betainc = require( '@stdlib/math/base/special/betainc' );

var opts = {
    'dtype': 'float64'
};
var x = 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( 'x: %0.4f, \t a: %0.4f, \t b: %0.4f, \t f(x,a,b): %0.4f', x, a, b, betainc );

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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.