{"id":15578437,"url":"https://github.com/stdlib-js/stats-incr-skewness","last_synced_at":"2025-04-24T02:22:44.888Z","repository":{"id":41370612,"uuid":"377239026","full_name":"stdlib-js/stats-incr-skewness","owner":"stdlib-js","description":"Compute a corrected sample skewness incrementally.","archived":false,"fork":false,"pushed_at":"2025-04-07T00:43:32.000Z","size":1087,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":3,"default_branch":"main","last_synced_at":"2025-04-11T21:10:01.754Z","etag":null,"topics":["accumulator","corrected","incremental","javascript","math","mathematics","node","node-js","nodejs","sample-skewness","shape","skewness","statistics","stats","stdlib"],"latest_commit_sha":null,"homepage":"https://github.com/stdlib-js/stdlib","language":"JavaScript","has_issues":false,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/stdlib-js.png","metadata":{"files":{"readme":"README.md","changelog":"CHANGELOG.md","contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE","code_of_conduct":"CODE_OF_CONDUCT.md","threat_model":null,"audit":null,"citation":"CITATION.cff","codeowners":null,"security":"SECURITY.md","support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null},"funding":{"github":["stdlib-js"],"open_collective":"stdlib","tidelift":"npm/@stdlib/stdlib"}},"created_at":"2021-06-15T17:12:07.000Z","updated_at":"2025-04-07T00:37:20.000Z","dependencies_parsed_at":"2023-09-24T06:41:49.615Z","dependency_job_id":"e15ebca7-a70f-4eb7-8da3-4f46b0b77c37","html_url":"https://github.com/stdlib-js/stats-incr-skewness","commit_stats":{"total_commits":49,"total_committers":1,"mean_commits":49.0,"dds":0.0,"last_synced_commit":"7d060ef6b879ea8c1f2bb34c7e306bda08bea269"},"previous_names":[],"tags_count":22,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-incr-skewness","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-incr-skewness/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-incr-skewness/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-incr-skewness/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/stdlib-js","download_url":"https://codeload.github.com/stdlib-js/stats-incr-skewness/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":250546452,"owners_count":21448335,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["accumulator","corrected","incremental","javascript","math","mathematics","node","node-js","nodejs","sample-skewness","shape","skewness","statistics","stats","stdlib"],"created_at":"2024-10-02T19:10:28.981Z","updated_at":"2025-04-24T02:22:44.867Z","avatar_url":"https://github.com/stdlib-js.png","language":"JavaScript","funding_links":["https://github.com/sponsors/stdlib-js","https://opencollective.com/stdlib","https://tidelift.com/funding/github/npm/@stdlib/stdlib"],"categories":[],"sub_categories":[],"readme":"\u003c!--\n\n@license Apache-2.0\n\nCopyright (c) 2018 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n--\u003e\n\n\n\u003cdetails\u003e\n  \u003csummary\u003e\n    About stdlib...\n  \u003c/summary\u003e\n  \u003cp\u003eWe 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.\u003c/p\u003e\n  \u003cp\u003eThe 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.\u003c/p\u003e\n  \u003cp\u003eWhen 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.\u003c/p\u003e\n  \u003cp\u003eTo join us in bringing numerical computing to the web, get started by checking us out on \u003ca href=\"https://github.com/stdlib-js/stdlib\"\u003eGitHub\u003c/a\u003e, and please consider \u003ca href=\"https://opencollective.com/stdlib\"\u003efinancially supporting stdlib\u003c/a\u003e. We greatly appreciate your continued support!\u003c/p\u003e\n\u003c/details\u003e\n\n# incrskewness\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \u003c!-- [![dependencies][dependencies-image]][dependencies-url] --\u003e\n\n\u003e Compute a [corrected sample skewness][sample-skewness] incrementally.\n\n\u003csection class=\"intro\"\u003e\n\nThe [skewness][sample-skewness] for a random variable `X` is defined as\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:skewness\" align=\"center\" raw=\"\\operatorname{Skewness}[X] = \\mathrm{E}\\biggl[ \\biggl( \\frac{X - \\mu}{\\sigma} \\biggr)^3 \\biggr]\" alt=\"Equation for skewness.\"\u003e --\u003e\n\n```math\n\\mathop{\\mathrm{Skewness}}[X] = \\mathrm{E}\\biggl[ \\biggl( \\frac{X - \\mu}{\\sigma} \\biggr)^3 \\biggr]\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"\\operatorname{Skewness}[X] = \\mathrm{E}\\biggl[ \\biggl( \\frac{X - \\mu}{\\sigma} \\biggr)^3 \\biggr]\" data-equation=\"eq:skewness\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/skewness/docs/img/equation_skewness.svg\" alt=\"Equation for skewness.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nFor a sample of `n` values, the [sample skewness][sample-skewness] is\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:sample_skewness\" align=\"center\" raw=\"b_1 = \\frac{m_3}{s^3} = \\frac{\\frac{1}{n} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^3}{\\biggl( \\frac{1}{n-1} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^2 \\biggr)^{3/2}}\" alt=\"Equation for the sample skewness.\"\u003e --\u003e\n\n```math\nb_1 = \\frac{m_3}{s^3} = \\frac{\\frac{1}{n} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^3}{\\biggl( \\frac{1}{n-1} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^2 \\biggr)^{3/2}}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"b_1 = \\frac{m_3}{s^3} = \\frac{\\frac{1}{n} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^3}{\\biggl( \\frac{1}{n-1} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^2 \\biggr)^{3/2}}\" data-equation=\"eq:sample_skewness\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/skewness/docs/img/equation_sample_skewness.svg\" alt=\"Equation for the sample skewness.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere `m_3` is the sample third central moment and `s` is the sample standard deviation.\n\nAn alternative definition for the [sample skewness][sample-skewness] which includes an adjustment factor (and is the implemented definition) is\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:adjusted_sample_skewness\" align=\"center\" raw=\"G_1 = \\frac{n^2}{(n-1)(n-2)} \\frac{m_3}{s^3} = \\frac{\\sqrt{n(n-1)}}{n-2} \\frac{\\frac{1}{n} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^3}{\\biggl( \\frac{1}{n} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^2 \\biggr)^{3/2}}\" alt=\"Equation for the adjusted sample skewness.\"\u003e --\u003e\n\n```math\nG_1 = \\frac{n^2}{(n-1)(n-2)} \\frac{m_3}{s^3} = \\frac{\\sqrt{n(n-1)}}{n-2} \\frac{\\frac{1}{n} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^3}{\\biggl( \\frac{1}{n} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^2 \\biggr)^{3/2}}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"G_1 = \\frac{n^2}{(n-1)(n-2)} \\frac{m_3}{s^3} = \\frac{\\sqrt{n(n-1)}}{n-2} \\frac{\\frac{1}{n} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^3}{\\biggl( \\frac{1}{n} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^2 \\biggr)^{3/2}}\" data-equation=\"eq:adjusted_sample_skewness\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/skewness/docs/img/equation_adjusted_sample_skewness.svg\" alt=\"Equation for the adjusted sample skewness.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003csection class=\"installation\"\u003e\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-incr-skewness\n```\n\nAlternatively,\n\n-   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]).\n-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).\n-   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]).\n\nThe [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.\n\nTo 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.\n\n\u003c/section\u003e\n\n\u003csection class=\"usage\"\u003e\n\n## Usage\n\n```javascript\nvar incrskewness = require( '@stdlib/stats-incr-skewness' );\n```\n\n#### incrskewness()\n\nReturns an accumulator `function` which incrementally computes a [corrected sample skewness][sample-skewness].\n\n```javascript\nvar accumulator = incrskewness();\n```\n\n#### accumulator( \\[x] )\n\nIf provided an input value `x`, the accumulator function returns an updated [corrected sample skewness][sample-skewness]. If not provided an input value `x`, the accumulator function returns the current [corrected sample skewness][sample-skewness].\n\n```javascript\nvar accumulator = incrskewness();\n\nvar skewness = accumulator();\n// returns null\n\nskewness = accumulator( 2.0 );\n// returns null\n\nskewness = accumulator( -5.0 );\n// returns null\n\nskewness = accumulator( -10.0 );\n// returns ~0.492\n\nskewness = accumulator();\n// returns ~0.492\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003csection class=\"notes\"\u003e\n\n## Notes\n\n-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **all** future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.\n\n\u003c/section\u003e\n\n\u003c!-- /.notes --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar randu = require( '@stdlib/random-base-randu' );\nvar incrskewness = require( '@stdlib/stats-incr-skewness' );\n\nvar accumulator;\nvar v;\nvar i;\n\n// Initialize an accumulator:\naccumulator = incrskewness();\n\n// For each simulated datum, update the corrected sample skewness...\nfor ( i = 0; i \u003c 100; i++ ) {\n    v = randu() * 100.0;\n    accumulator( v );\n}\nconsole.log( accumulator() );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n* * *\n\n\u003csection class=\"references\"\u003e\n\n## References\n\n-   Joanes, D. N., and C. A. Gill. 1998. \"Comparing measures of sample skewness and kurtosis.\" _Journal of the Royal Statistical Society: Series D (The Statistician)_ 47 (1). Blackwell Publishers Ltd: 183–89. doi:[10.1111/1467-9884.00122][@joanes:1998].\n\n\u003c/section\u003e\n\n\u003c!-- /.references --\u003e\n\n\u003c!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --\u003e\n\n\u003csection class=\"related\"\u003e\n\n* * *\n\n## See Also\n\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-incr/kurtosis`][@stdlib/stats/incr/kurtosis]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecompute a corrected sample excess kurtosis incrementally.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-incr/mean`][@stdlib/stats/incr/mean]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecompute an arithmetic mean incrementally.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-incr/stdev`][@stdlib/stats/incr/stdev]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecompute a corrected sample standard deviation incrementally.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-incr/summary`][@stdlib/stats/incr/summary]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecompute a statistical summary incrementally.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-incr/variance`][@stdlib/stats/incr/variance]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecompute an unbiased sample variance incrementally.\u003c/span\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.related --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\n\u003csection class=\"main-repo\" \u003e\n\n* * *\n\n## Notice\n\nThis 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.\n\nFor 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].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright \u0026copy; 2016-2025. The Stdlib [Authors][stdlib-authors].\n\n\u003c/section\u003e\n\n\u003c!-- /.stdlib --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"links\"\u003e\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-incr-skewness.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-incr-skewness\n\n[test-image]: https://github.com/stdlib-js/stats-incr-skewness/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/stats-incr-skewness/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-incr-skewness/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-incr-skewness?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-incr-skewness.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-incr-skewness/main\n\n--\u003e\n\n[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg\n[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/stats-incr-skewness/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-incr-skewness/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-incr-skewness/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-incr-skewness/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-incr-skewness/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-incr-skewness/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-incr-skewness/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-skewness/main/LICENSE\n\n[sample-skewness]: https://en.wikipedia.org/wiki/Skewness\n\n[@joanes:1998]: http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00122/\n\n\u003c!-- \u003crelated-links\u003e --\u003e\n\n[@stdlib/stats/incr/kurtosis]: https://github.com/stdlib-js/stats-incr-kurtosis\n\n[@stdlib/stats/incr/mean]: https://github.com/stdlib-js/stats-incr-mean\n\n[@stdlib/stats/incr/stdev]: https://github.com/stdlib-js/stats-incr-stdev\n\n[@stdlib/stats/incr/summary]: https://github.com/stdlib-js/stats-incr-summary\n\n[@stdlib/stats/incr/variance]: https://github.com/stdlib-js/stats-incr-variance\n\n\u003c!-- \u003c/related-links\u003e --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.links --\u003e\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-incr-skewness","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fstats-incr-skewness","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-incr-skewness/lists"}