Ecosyste.ms: Awesome
An open API service indexing awesome lists of open source software.
https://github.com/stdlib-js/stats-base-dists-normal
Normal distribution.
https://github.com/stdlib-js/stats-base-dists-normal
continuous dist distribution javascript lib library node node-js nodejs normal probability standard statistics stats stdlib univariate
Last synced: 3 days ago
JSON representation
Normal distribution.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-base-dists-normal
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:33:23.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-12-01T05:21:01.000Z (about 1 month ago)
- Last Synced: 2024-12-01T06:30:40.822Z (about 1 month ago)
- Topics: continuous, dist, distribution, javascript, lib, library, node, node-js, nodejs, normal, probability, standard, statistics, stats, stdlib, univariate
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 2.1 MB
- Stars: 2
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
Awesome Lists containing this project
README
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!
# Normal
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Normal distribution.
## Installation
```bash
npm install @stdlib/stats-base-dists-normal
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var normal = require( '@stdlib/stats-base-dists-normal' );
```
#### normal
Normal distribution.
```javascript
var dist = normal;
// returns {...}
```
The namespace contains the following distribution functions:
- [`cdf( x, mu, sigma )`][@stdlib/stats/base/dists/normal/cdf]: normal distribution cumulative distribution function.
- [`logcdf( x, mu, sigma )`][@stdlib/stats/base/dists/normal/logcdf]: evaluate the natural logarithm of the cumulative distribution function (CDF) for a normal distribution.
- [`logpdf( x, mu, sigma )`][@stdlib/stats/base/dists/normal/logpdf]: evaluate the natural logarithm of the probability density function (PDF) for a normal distribution.
- [`mgf( t, mu, sigma )`][@stdlib/stats/base/dists/normal/mgf]: normal distribution moment-generating function (MGF).
- [`pdf( x, mu, sigma )`][@stdlib/stats/base/dists/normal/pdf]: normal distribution probability density function (PDF).
- [`quantile( p, mu, sigma )`][@stdlib/stats/base/dists/normal/quantile]: normal distribution quantile function.
The namespace contains the following functions for calculating distribution properties:
- [`entropy( mu, sigma )`][@stdlib/stats/base/dists/normal/entropy]: normal distribution differential entropy.
- [`kurtosis( mu, sigma )`][@stdlib/stats/base/dists/normal/kurtosis]: normal distribution excess kurtosis.
- [`mean( mu, sigma )`][@stdlib/stats/base/dists/normal/mean]: normal distribution expected value.
- [`median( mu, sigma )`][@stdlib/stats/base/dists/normal/median]: normal distribution median.
- [`mode( mu, sigma )`][@stdlib/stats/base/dists/normal/mode]: normal distribution mode.
- [`skewness( mu, sigma )`][@stdlib/stats/base/dists/normal/skewness]: normal distribution skewness.
- [`stdev( mu, sigma )`][@stdlib/stats/base/dists/normal/stdev]: normal distribution standard deviation.
- [`variance( mu, sigma )`][@stdlib/stats/base/dists/normal/variance]: normal distribution variance.
The namespace contains a constructor function for creating a [normal][normal-distribution] distribution object.
- [`Normal( [mu, sigma] )`][@stdlib/stats/base/dists/normal/ctor]: normal distribution constructor.
```javascript
var Normal = require( '@stdlib/stats-base-dists-normal' ).Normal;
var dist = new Normal( 2.0, 4.0 );
var y = dist.pdf( 2.0 );
// returns ~0.1
```
## Examples
```javascript
var normal = require( '@stdlib/stats-base-dists-normal' );
/*
A bakery is analyzing cake baking times to ensure consistency and better schedule their baking processes.
The Central Limit Theorem (CLT) states that the average baking times from many batches will follow a normal distribution if there are enough batches (typically n > 30).
Assuming each record represents the average baking time per batch and the bakery has collected the following data:
- Mean baking time (μ/mu): 20 minutes.
- Standard deviation in baking time (σ/sigma): 3 minutes.
We can model the average bake times using a normal distribution with μ (mu) = 20.0 minutes and σ = 3.0 minutes.
*/
var mu = 20.0;
var sigma = 3.0;
var normalDist = new normal.Normal( mu, sigma );
// Output the standard deviation of the baking times:
console.log( normalDist.sigma );
// => 3.0
// Adjust distribution parameters
normalDist.sigma = 4.0;
// Adjusted standard deviation to reflect different variance scenario:
console.log( normalDist.sigma );
// => 4.0
// Excess kurtosis of a normal distribution (measure of "tailedness"):
console.log( normalDist.kurtosis );
// => 0.0
// Median baking time:
console.log( normalDist.median );
// => 20.0
// Variance of the baking times after adjusting sigma:
console.log( normalDist.variance );
// => 16.0
// Probability density function at the mean baking time:
console.log( normal.pdf( 20.0, mu, sigma ) );
// => ~0.133
// Cumulative distribution function at the mean (portion of times ≤ 20 minutes):
console.log( normal.cdf( 20.0, mu, sigma ) );
// => ~0.5
// 50th percentile (median) of the baking times:
console.log( normal.quantile( 0.5, mu, sigma ) );
// => 20.0
// Moment-generating function value at 0.5 (used in probability theory):
console.log( normal.mgf( 0.5, mu, sigma ) );
// => ~67846.291
// Entropy of the normal distribution (measure of uncertainty):
console.log( normal.entropy( mu, sigma ) );
// => ~2.518
// Mean baking time:
console.log( normal.mean( mu, sigma ) );
// => 20.0
// Median baking time:
console.log( normal.median( mu, sigma ) );
// => 20.0
// Mode of the baking times (most frequent value):
console.log( normal.mode( mu, sigma ) );
// => 20.0
// Variance of the baking times:
console.log( normal.variance( mu, sigma ) );
// => 9.0
// Skewness of the distribution (symmetry measure):
console.log( normal.skewness( mu, sigma ) );
// => 0.0
var myquantile = normal.quantile.factory( 20.0, 3.0 );
// 20th percentile (value below which 20% baking times fall):
console.log( myquantile( 0.2 ) );
// => ~17.475
// 80th percentile (value below which 80% baking times fall):
console.log( myquantile( 0.8 ) );
// => ~22.525
var mylogpdf = normal.logpdf.factory( 20.0, 3.0 );
// Logarithm of the probability density function at the mean:
console.log( mylogpdf( 20.0 ) );
// => ~-2.018
// Logarithm of the probability density function at 15 minutes:
console.log( mylogpdf( 15.0 ) );
// => ~-3.406
```
* * *
## 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 © 2016-2024. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-normal.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-normal
[test-image]: https://github.com/stdlib-js/stats-base-dists-normal/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-base-dists-normal/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-normal/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-normal?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[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/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-normal/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-normal/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-normal/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-normal/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-normal/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-normal/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-normal/main/LICENSE
[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution
[@stdlib/stats/base/dists/normal/ctor]: https://github.com/stdlib-js/stats-base-dists-normal-ctor
[@stdlib/stats/base/dists/normal/entropy]: https://github.com/stdlib-js/stats-base-dists-normal-entropy
[@stdlib/stats/base/dists/normal/kurtosis]: https://github.com/stdlib-js/stats-base-dists-normal-kurtosis
[@stdlib/stats/base/dists/normal/mean]: https://github.com/stdlib-js/stats-base-dists-normal-mean
[@stdlib/stats/base/dists/normal/median]: https://github.com/stdlib-js/stats-base-dists-normal-median
[@stdlib/stats/base/dists/normal/mode]: https://github.com/stdlib-js/stats-base-dists-normal-mode
[@stdlib/stats/base/dists/normal/skewness]: https://github.com/stdlib-js/stats-base-dists-normal-skewness
[@stdlib/stats/base/dists/normal/stdev]: https://github.com/stdlib-js/stats-base-dists-normal-stdev
[@stdlib/stats/base/dists/normal/variance]: https://github.com/stdlib-js/stats-base-dists-normal-variance
[@stdlib/stats/base/dists/normal/cdf]: https://github.com/stdlib-js/stats-base-dists-normal-cdf
[@stdlib/stats/base/dists/normal/logcdf]: https://github.com/stdlib-js/stats-base-dists-normal-logcdf
[@stdlib/stats/base/dists/normal/logpdf]: https://github.com/stdlib-js/stats-base-dists-normal-logpdf
[@stdlib/stats/base/dists/normal/mgf]: https://github.com/stdlib-js/stats-base-dists-normal-mgf
[@stdlib/stats/base/dists/normal/pdf]: https://github.com/stdlib-js/stats-base-dists-normal-pdf
[@stdlib/stats/base/dists/normal/quantile]: https://github.com/stdlib-js/stats-base-dists-normal-quantile