Quantile Function

Arcsine distribution quantile function.

The quantile function for an arcsine random variable is

upper Q left-parenthesis p right-parenthesis equals a plus left-parenthesis b minus a right-parenthesis sine squared left-parenthesis StartFraction pi Over 2 EndFraction p right-parenthesis

for 0 <= p <= 1, where a is the minimum support and b is the maximum support. The parameters must satisfy a < b.

Usage

var quantile = require( '@stdlib/math/base/dists/arcsine/quantile' );

quantile( p, a, b )

Evaluates the quantile function for an arcsine distribution with parameters a (minimum support) and b (maximum support).

var y = quantile( 0.8, 0.0, 1.0 );
// returns ~0.905

y = quantile( 0.5, 0.0, 10.0 );
// returns ~5.0

If provided a probability p outside the interval [0,1], the function returns NaN.

var y = quantile( 1.9, 0.0, 1.0 );
// returns NaN

y = quantile( -0.1, 0.0, 1.0 );
// returns NaN

If provided NaN as any argument, the function returns NaN.

var y = quantile( NaN, 0.0, 1.0 );
// returns NaN

y = quantile( 0.0, NaN, 1.0 );
// returns NaN

y = quantile( 0.0, 0.0, NaN );
// returns NaN

If provided a >= b, the function returns NaN.

var y = quantile( 0.4, 2.0, 1.0 );
// returns NaN

quantile.factory( a, b )

Returns a function for evaluating the quantile function of an arcsine distribution with parameters a (minimum support) and b (maximum support).

var myquantile = quantile.factory( 0.0, 4.0 );
y = myquantile( 0.8 );
// returns ~3.618

Examples

var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/math/base/dists/arcsine/quantile' );

var a;
var b;
var p;
var y;
var i;

for ( i = 0; i < 25; i++ ) {
    p = randu();
    a = ( randu()*20.0 ) - 20.0;
    b = a + ( randu()*40.0 );
    y = quantile( p, a, b );
    console.log( 'p: %d, a: %d, b: %d, Q(p;a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}