Quantile Function

Lévy distribution quantile function.

The quantile function for a Lévy random variable is

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

Installation

npm install @stdlib/stats-base-dists-levy-quantile

Usage

var quantile = require( '@stdlib/stats-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/stats-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 );
}

C APIs

Usage

#include "stdlib/stats/base/dists/levy/quantile.h"

stdlib_base_dists_levy_quantile( p, mu, c )

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

double out = stdlib_base_dists_levy_quantile( 0.8, 0.0, 1.0 );
// returns ~15.58

The function accepts the following arguments:

• p: [in] double probability.
• mu: [in] double location parameter.
• c: [in] double scale parameter.

double stdlib_base_dists_levy_quantile( const double p, const double mu, const double c );

Examples

#include "stdlib/stats/base/dists/levy/quantile.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double mu;
    double p;
    double c;
    double y;
    int i;
    for ( i = 0; i < 25; i++ ) {
        p = random_uniform( 0.0, 1.0 );
        mu = random_uniform( 0.0, 10.0 );
        c = random_uniform( 0.0, 10.0 );
        y = stdlib_base_dists_levy_quantile( p, mu, c );
        printf( "p: %lf, µ: %lf, c: %lf, Q(p;µ,c): %lf\n", p, mu, c, y );
    }
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.