Quantile Function

Normal distribution quantile function.

The quantile function for a normal random variable is

for 0 <= p <= 1, where µ is the mean and σ is the standard deviation.

Installation

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

Usage

var quantile = require( '@stdlib/stats-base-dists-normal-quantile' );

quantile( p, mu, sigma )

Evaluates the quantile function for a normal distribution with parameters mu (mean) and sigma (standard deviation).

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

y = quantile( 0.2, 4.0, 2.0 );
// returns ~2.317

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 sigma < 0, the function returns NaN.

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

If provided sigma = 0, the function evaluates the quantile function of a degenerate distribution centered at mu.

var y = quantile( 0.3, 8.0, 0.0 );
// returns 8.0

y = quantile( 0.9, 8.0, 0.0 );
// returns 8.0

quantile.factory( mu, sigma )

Returns a function for evaluating the quantile function of a normal distribution with parameters mu and sigma.

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

var y = myquantile( 0.2 );
// returns ~8.317

y = myquantile( 0.8 );
// returns ~11.683

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var quantile = require( '@stdlib/stats-base-dists-normal-quantile' );

var opts = {
    'dtype': 'float64'
};
var sigma = uniform( 10, 0.0, 20.0, opts );
var mu = uniform( 10, -5.0, 5.0, opts );
var p = uniform( 10, 0.0, 1.0, opts );

logEachMap( 'p: %0.4f, µ: %0.4f, σ: %0.4f, Q(p;µ,σ): %0.4f', p, mu, sigma, quantile );

C APIs

Usage

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

stdlib_base_dists_normal_quantile( p, mu, sigma )

Evaluates the quantile function for a normal distribution with parameters mu (mean) and sigma (standard deviation).

double y = stdlib_base_dists_normal_quantile( 0.8, 0.0, 1.0 );
// returns ~0.842

The function accepts the following arguments:

• p: [in] double probability.
• mu: [in] double mean.
• sigma: [in] double standard deviation.

double stdlib_base_dists_normal_quantile( const double p, const double mu, const double sigma );

Examples

#include "stdlib/stats/base/dists/normal/quantile.h"
#include "stdlib/constants/float64/eps.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 sigma;
    double mu;
    double p;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        p = random_uniform( 0.0, 1.0 );
        mu = random_uniform( -5.0, 5.0 );
        sigma = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
        y = stdlib_base_dists_normal_quantile( p, mu, sigma );
        printf( "p:%.4f, µ: %.4f, σ: %.4f, Q(p;µ,σ): %.4f\n", p, mu, sigma, 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.