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stats-array-stdevwd

Calculate the standard deviation of an array using Welford's algorithm.

https://github.com/stdlib-js/stats-array-stdevwd

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array deviation dispersion javascript math mathematics node node-js nodejs sample-standard-deviation spread standard-deviation statistics stats stdlib unbiased var variance
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Calculate the standard deviation of an array using Welford's algorithm.

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array deviation dispersion javascript math mathematics node node-js nodejs sample-standard-deviation spread standard-deviation statistics stats stdlib unbiased var variance
Created 6 months ago · Last pushed 6 months ago
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README.md

About stdlib...

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stdevwd

NPM version Build Status Coverage Status <!-- dependencies -->

Calculate the standard deviation of an array using Welford's algorithm.

The population [standard deviation][standard-deviation] of a finite size population of size `N` is given by ```math \sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} ``` where the population mean is given by ```math \mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i ``` Often in the analysis of data, the true population [standard deviation][standard-deviation] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [standard deviation][standard-deviation], the result is biased and yields an **uncorrected sample standard deviation**. To compute a **corrected sample standard deviation** for a sample of size `n`, ```math s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} ``` where the sample mean is given by ```math \bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i ``` The use of the term `n-1` is commonly referred to as Bessel's correction. Note, however, that applying Bessel's correction can increase the mean squared error between the sample standard deviation and population standard deviation. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.
## Installation ```bash npm install @stdlib/stats-array-stdevwd ``` 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 stdevwd = require( '@stdlib/stats-array-stdevwd' ); ``` #### stdevwd( x\[, correction] ) Computes the [standard deviation][standard-deviation] of an array using Welford's algorithm. ```javascript var x = [ 1.0, -2.0, 2.0 ]; var v = stdevwd( x ); // returns ~2.0817 ``` The function has the following parameters: - **x**: input array. - **correction**: degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [standard deviation][standard-deviation] according to `N-c` where `N` corresponds to the number of array elements and `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the unbiased sample [standard deviation][standard-deviation], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction). Default: `1.0`. By default, the function computes the sample [standard deviation][standard-deviation]. To adjust the degrees of freedom when computing the [standard deviation][standard-deviation], provide a `correction` argument. ```javascript var x = [ 1.0, -2.0, 2.0 ]; var v = stdevwd( x, 0.0 ); // returns ~1.6997 ```
## Notes - If provided an empty array, the function returns `NaN`. - If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), the function returns `NaN`. - The function supports array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array-base/accessor`][@stdlib/array/base/accessor]).
## Examples ```javascript var discreteUniform = require( '@stdlib/random-array-discrete-uniform' ); var stdevwd = require( '@stdlib/stats-array-stdevwd' ); var x = discreteUniform( 10, -50, 50, { 'dtype': 'float64' }); console.log( x ); var v = stdevwd( x ); console.log( v ); ```
## References - Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3). Taylor & Francis: 419–20. doi:[10.1080/00401706.1962.10490022][@welford:1962a]. - van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11 (3): 149–50. doi:[10.1145/362929.362961][@vanreeken:1968a].
* * * ## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].

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Standard library for JavaScript.

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cff-version: 1.2.0
title: stdlib
message: >-
  If you use this software, please cite it using the
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type: software

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

repository-code: https://github.com/stdlib-js/stdlib
url: https://stdlib.io

abstract: |
  Standard library for JavaScript and Node.js.

keywords:
  - JavaScript
  - Node.js
  - TypeScript
  - standard library
  - scientific computing
  - numerical computing
  - statistical computing

license: Apache-2.0 AND BSL-1.0

date-released: 2016

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