Quantile Function

Lévy distribution quantile function.

The quantile function for a Lévy random variable is

upper Q left-parenthesis p semicolon mu comma c right-parenthesis equals mu plus StartFraction c Over 2 dot e r f c i n v left-parenthesis p right-parenthesis squared EndFraction

for 0 <= p < 1, where µ is the location parameter and c > 0 is the scale parameter.

Usage

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

quantile( p, mu, c )

Evaluates the quantile function for a Lévy distribution with parameters mu (location parameter) and c (scale parameter).

var y = quantile( 0.5, 0.0, 1.0 );
// returns ~2.198

y = quantile( 0.2, 4.0, 2.0 );
// returns ~5.218

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 c <= 0, the function returns NaN.

var y = quantile( 0.4, 0.0, -1.0 );
// returns NaN

y = quantile( 0.4, 0.0, 0.0 );
// returns NaN

quantile.factory( mu, c )

Returns a function for evaluating the quantile function of a Lévy distribution with parameters mu and c.

var myQuantile = quantile.factory( 10.0, 2.0 );

var y = myQuantile( 0.2 );
// returns ~11.218

y = myQuantile( 0.8 );
// returns ~41.16

Examples

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

var mu;
var c;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    mu = randu() * 10.0;
    c = randu() * 10.0;
    y = quantile( p, mu, c );
    console.log( 'p: %d, µ: %d, c: %d, Q(p;µ,c): %d', p, mu, c, y );
}