About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Quantile Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> [Normal][normal-distribution] distribution [quantile function][quantile-function].

The [quantile function][quantile-function] for a [normal][normal-distribution] random variable is

Quantile function for a Normal distribution.

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

Installation

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

`Usage`

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

#### quantile( p, mu, sigma )

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

`javascript 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.

`javascript 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.

`javascript 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.

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

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

`javascript 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][quantile-function] of a [normal][normal-distribution] distribution with parameters mu and sigma.

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

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

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

`Examples`

`javascript 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`

`$3`

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

#### stdlib_base_dists_normal_quantile( p, mu, sigma )

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

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

The function accepts the following arguments:

- p: [in] doubleprobability. - mu:[in] doublemean. - sigma:[in] double standard deviation.

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

`$3`

`c #include "stdlib/stats/base/dists/normal/quantile.h" #include "stdlib/constants/float64/eps.h" #include #include

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][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][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

`License`

See [LICENSE][stdlib-license].

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-normal-quantile.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-normal-quantile

[test-image]: https://github.com/stdlib-js/stats-base-dists-normal-quantile/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/stats-base-dists-normal-quantile/actions/workflows/test.yml?query=branch:v0.3.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-normal-quantile/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-normal-quantile?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/stats-base-dists-normal-quantile/tree/deno [deno-readme]: https://github.com/stdlib-js/stats-base-dists-normal-quantile/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/stats-base-dists-normal-quantile/tree/umd [umd-readme]: https://github.com/stdlib-js/stats-base-dists-normal-quantile/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/stats-base-dists-normal-quantile/tree/esm [esm-readme]: https://github.com/stdlib-js/stats-base-dists-normal-quantile/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/stats-base-dists-normal-quantile/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-normal-quantile/main/LICENSE

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution


  
    About stdlib...
  

  We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

  The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

  When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

  To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

`Quantile Function`

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> [Normal][normal-distribution] distribution [quantile function][quantile-function].

The [quantile function][quantile-function] for a [normal][normal-distribution] random variable is

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

`Installation`

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

`Usage`

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

#### quantile( p, mu, sigma )

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

`javascript 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.

`javascript 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.

`javascript 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.

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

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

`javascript 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][quantile-function] of a [normal][normal-distribution] distribution with parameters mu and sigma.

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

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

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

`Examples`

`javascript 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`

`$3`

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

#### stdlib_base_dists_normal_quantile( p, mu, sigma )

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

`c 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.

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

`$3`

`c #include "stdlib/stats/base/dists/normal/quantile.h" #include "stdlib/constants/float64/eps.h" #include #include

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`

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

#### Community

[![Chat][chat-image]][chat-url]

---

`License`

See [LICENSE][stdlib-license].

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-normal-quantile.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-normal-quantile

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-normal-quantile/main/LICENSE

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution