@stdlib/stats-base-dists-normal-cdf
v0.3.1TypeScript
Normal distribution cumulative distribution function (CDF).
stdlibstdmathstatisticsstatsdistributiondistprobabilitycdfcumulative distributiondistribution function
0/weekUpdated yesterdayApache-2.0Unpacked: 56.3 KB
Published by The Stdlib Authors
npm install @stdlib/stats-base-dists-normal-cdfWe 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!
About stdlib...
Cumulative Distribution Function
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> [Normal][normal-distribution] distribution [cumulative distribution function][cdf].
The [cumulative distribution function][cdf] for a [normal][normal-distribution] random variable is
where µ is the mean and σ is the standard deviation.
Installation
``bash`
npm install @stdlib/stats-base-dists-normal-cdf
Usage
`javascript`
var cdf = require( '@stdlib/stats-base-dists-normal-cdf' );
#### cdf( x, mu, sigma )
Evaluates the [cumulative distribution function][cdf] (CDF) for a [normal][normal-distribution] distribution with parameters mu (mean) and sigma (standard deviation).
`javascript
var y = cdf( 2.0, 0.0, 1.0 );
// returns ~0.977
y = cdf( 0.0, 0.0, 1.0 );
// returns 0.5
y = cdf( -1.0, 4.0, 2.0 );
// returns ~0.006
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = cdf( NaN, 0.0, 1.0 );
// returns NaN
y = cdf( 0.0, NaN, 1.0 );
// returns NaN
y = cdf( 0.0, 0.0, NaN );
// returns NaN
`
If provided sigma < 0, the function returns NaN.
`javascript`
var y = cdf( 2.0, 0.0, -1.0 );
// returns NaN
If provided sigma = 0, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at mu.
`javascript
var y = cdf( 2.0, 8.0, 0.0 );
// returns 0.0
y = cdf( 8.0, 8.0, 0.0 );
// returns 1.0
y = cdf( 10.0, 8.0, 0.0 );
// returns 1.0
`
#### cdf.factory( mu, sigma )
Returns a function for evaluating the [cumulative distribution function][cdf] of a normal distribution with parameters mu and sigma.
`javascript
var mycdf = cdf.factory( 10.0, 2.0 );
var y = mycdf( 10.0 );
// returns 0.5
y = mycdf( 8.0 );
// returns ~0.159
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-normal-cdf' );
var opts = {
'dtype': 'float64'
};
var sigma = uniform( 10, 0.0, 20.0, opts );
var mu = uniform( 10, -5.0, 5.0, opts );
var x = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, µ: %0.4f, σ: %0.4f, F(x;µ,σ): %0.4f', x, mu, sigma, cdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/normal/cdf.h"
#### stdlib_base_dists_normal_cdf( x, a, b )
Evaluates the [cumulative distribution function][cdf] (CDF) for a [normal][normal-distribution] distribution with parameters mu (mean) and sigma (standard deviation).
`c`
double out = stdlib_base_dists_normal_cdf( 2.0, 0.0, 1.0 );
// returns ~0.977
The function accepts the following arguments:
- x: [in] double input value.[in] double
- mu: mean.[in] double
- sigma: standard deviation.
`c`
double stdlib_base_dists_normal_cdf( cconst double x, const double mu, const double sigma );
$3
`c
#include "stdlib/stats/base/dists/normal/cdf.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 x;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
x = random_uniform( 0.0, 10.0 );
mu = random_uniform( -5.0, 5.0 );
sigma = random_uniform( 0.1, 20.0 );
y = stdlib_base_dists_normal_cdf( x, mu, sigma );
printf( "x: %lf, µ: %lf, σ: %lf, F(x;µ,σ): %lf\n", x, 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
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-normal-cdf.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-normal-cdf
[test-image]: https://github.com/stdlib-js/stats-base-dists-normal-cdf/actions/workflows/test.yml/badge.svg?branch=v0.3.1
[test-url]: https://github.com/stdlib-js/stats-base-dists-normal-cdf/actions/workflows/test.yml?query=branch:v0.3.1
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-normal-cdf/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-normal-cdf?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-cdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-normal-cdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-normal-cdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-normal-cdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-normal-cdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-normal-cdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-normal-cdf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-normal-cdf/main/LICENSE
[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution
[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution