betaincinv
Inverse of the incomplete beta function.
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 ) );
}