Quantile Function

Kumaraswamy's double bounded distribution quantile function.

The quantile function for a Kumaraswamy's double bounded random variable is

upper Q left-parenthesis p semicolon a comma b right-parenthesis equals left-parenthesis 1 minus left-parenthesis 1 minus p right-parenthesis Superscript StartFraction 1 Over b EndFraction Baseline right-parenthesis Superscript StartFraction 1 Over a EndFraction

for 0 <= p <= 1, where a > 0 is the first shape parameter and b > 0 is the second shape parameter.

Usage

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

quantile( p, a, b )

Evaluates the quantile function for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

var y = quantile( 0.5, 1.0, 1.0 );
// returns 0.5

y = quantile( 0.5, 2.0, 4.0 );
// returns ~0.399

y = quantile( 0.2, 2.0, 2.0 );
// returns ~0.325

y = quantile( 0.8, 4.0, 4.0 );
// returns ~0.759

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

var y = quantile( -0.5, 4.0, 2.0 );
// returns NaN

y = quantile( 1.5, 4.0, 2.0 );
// returns NaN

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

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

y = quantile( 0.2, NaN, 1.0 );
// returns NaN

y = quantile( 0.2, 1.0, NaN );
// returns NaN

If provided a <= 0, the function returns NaN.

var y = quantile( 0.2, -1.0, 0.5 );
// returns NaN

y = quantile( 0.2, 0.0, 0.5 );
// returns NaN

If provided b <= 0, the function returns NaN.

var y = quantile( 0.2, 0.5, -1.0 );
// returns NaN

y = quantile( 0.2, 0.5, 0.0 );
// returns NaN

quantile.factory( a, b )

Returns a function for evaluating the quantile function for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

var myQuantile = quantile.factory( 0.5, 0.5 );

var y = myQuantile( 0.8 );
// returns ~0.922

y = myQuantile( 0.3 );
// returns ~0.26

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var quantile = require( '@stdlib/math/base/dists/kumaraswamy/quantile' );

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

for ( i = 0; i < 10; i++ ) {
    p = randu();
    a = ( randu()*5.0 ) + EPS;
    b = ( randu()*5.0 ) + EPS;
    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 ) );
}