{"id":19472071,"url":"https://github.com/stdlib-js/stats-incr-mvmr","last_synced_at":"2025-06-19T18:36:57.132Z","repository":{"id":41410336,"uuid":"376838439","full_name":"stdlib-js/stats-incr-mvmr","owner":"stdlib-js","description":"Compute a moving variance-to-mean ratio (VMR) incrementally.","archived":false,"fork":false,"pushed_at":"2025-01-20T02:06:22.000Z","size":923,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":3,"default_branch":"main","last_synced_at":"2025-04-20T03:32:59.424Z","etag":null,"topics":["dispersion","dispersion-index","fano","fano-factor","index-of-dispersion","javascript","math","mathematics","node","node-js","nodejs","relative-variance","sample","sample-variance","statistics","stats","stdlib","unbiased","variance","vmr"],"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":"2021-06-14T13:46:37.000Z","updated_at":"2025-01-20T01:45:52.000Z","dependencies_parsed_at":"2023-02-17T06:46:11.552Z","dependency_job_id":"2f776722-88b3-43e1-b5c1-aaff299562a5","html_url":"https://github.com/stdlib-js/stats-incr-mvmr","commit_stats":{"total_commits":50,"total_committers":1,"mean_commits":50.0,"dds":0.0,"last_synced_commit":"26f36698554d774acb3d4bc0c30c443876db919d"},"previous_names":[],"tags_count":23,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-incr-mvmr","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-incr-mvmr/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-incr-mvmr/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-incr-mvmr/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/stdlib-js","download_url":"https://codeload.github.com/stdlib-js/stats-incr-mvmr/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":250817619,"owners_count":21492186,"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":["dispersion","dispersion-index","fano","fano-factor","index-of-dispersion","javascript","math","mathematics","node","node-js","nodejs","relative-variance","sample","sample-variance","statistics","stats","stdlib","unbiased","variance","vmr"],"created_at":"2024-11-10T19:12:10.568Z","updated_at":"2025-04-25T12:31:19.809Z","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# incrmvmr\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 moving [variance-to-mean ratio][variance-to-mean-ratio] (VMR) incrementally.\n\n\u003csection class=\"intro\"\u003e\n\nFor a window of size `W`, the [unbiased sample variance][sample-variance] is defined as\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:unbiased_sample_variance\" align=\"center\" raw=\"s^2 = \\frac{1}{W-1} \\sum_{i=0}^{W-1} ( x_i - \\bar{x} )^2\" alt=\"Equation for the unbiased sample variance.\"\u003e --\u003e\n\n```math\ns^2 = \\frac{1}{W-1} \\sum_{i=0}^{W-1} ( x_i - \\bar{x} )^2\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"s^2 = \\frac{1}{W-1} \\sum_{i=0}^{W-1} ( x_i - \\bar{x} )^2\" data-equation=\"eq:unbiased_sample_variance\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@b331e5634fe726ff0e16e87814ac3f85d8164d31/lib/node_modules/@stdlib/stats/incr/mvmr/docs/img/equation_unbiased_sample_variance.svg\" alt=\"Equation for the unbiased sample variance.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nand the [arithmetic mean][arithmetic-mean] is defined as\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:arithmetic_mean\" align=\"center\" raw=\"\\bar{x} = \\frac{1}{W} \\sum_{i=0}^{W-1} x_i\" alt=\"Equation for the arithmetic mean.\"\u003e --\u003e\n\n```math\n\\bar{x} = \\frac{1}{W} \\sum_{i=0}^{W-1} x_i\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"\\bar{x} = \\frac{1}{W} \\sum_{i=0}^{W-1} x_i\" data-equation=\"eq:arithmetic_mean\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@164b8f1010c4535340eed9ad0b2af32c4a19863c/lib/node_modules/@stdlib/stats/incr/mvmr/docs/img/equation_arithmetic_mean.svg\" alt=\"Equation for the arithmetic mean.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nThe [variance-to-mean ratio][variance-to-mean-ratio] (VMR) is thus defined as\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:variance_to_mean_ratio\" align=\"center\" raw=\"F = \\frac{s^2}{\\bar{x}}\" alt=\"Equation for the variance-to-mean ratio (VMR).\"\u003e --\u003e\n\n```math\nF = \\frac{s^2}{\\bar{x}}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"F = \\frac{s^2}{\\bar{x}}\" data-equation=\"eq:variance_to_mean_ratio\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@b331e5634fe726ff0e16e87814ac3f85d8164d31/lib/node_modules/@stdlib/stats/incr/mvmr/docs/img/equation_variance_to_mean_ratio.svg\" alt=\"Equation for the variance-to-mean ratio (VMR).\"\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-mvmr\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 incrmvmr = require( '@stdlib/stats-incr-mvmr' );\n```\n\n#### incrmvmr( window\\[, mean] )\n\nReturns an accumulator `function` which incrementally computes a moving [variance-to-mean ratio][variance-to-mean-ratio]. The `window` parameter defines the number of values over which to compute the moving [variance-to-mean ratio][variance-to-mean-ratio].\n\n```javascript\nvar accumulator = incrmvmr( 3 );\n```\n\nIf the mean is already known, provide a `mean` argument.\n\n```javascript\nvar accumulator = incrmvmr( 3, 5.0 );\n```\n\n#### accumulator( \\[x] )\n\nIf provided an input value `x`, the accumulator function returns an updated accumulated value. If not provided an input value `x`, the accumulator function returns the current accumulated value.\n\n```javascript\nvar accumulator = incrmvmr( 3 );\n\nvar F = accumulator();\n// returns null\n\n// Fill the window...\nF = accumulator( 2.0 ); // [2.0]\n// returns 0.0\n\nF = accumulator( 1.0 ); // [2.0, 1.0]\n// returns ~0.33\n\nF = accumulator( 3.0 ); // [2.0, 1.0, 3.0]\n// returns 0.5\n\n// Window begins sliding...\nF = accumulator( 7.0 ); // [1.0, 3.0, 7.0]\n// returns ~2.55\n\nF = accumulator( 5.0 ); // [3.0, 7.0, 5.0]\n// returns ~0.80\n\nF = accumulator();\n// returns ~0.80\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 **at least** `W-1` 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-   As `W` values are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.\n\n-   The following table summarizes how to interpret the [variance-to-mean ratio][variance-to-mean-ratio]:\n\n    |        VMR        |   Description   |     Example Distribution     |\n    | :---------------: | :-------------: | :--------------------------: |\n    |         0         |  not dispersed  |           constant           |\n    | 0 \u0026lt; VMR \u0026lt; 1 | under-dispersed |           binomial           |\n    |         1         |        --       |            Poisson           |\n    |         \u003e1        |  over-dispersed | geometric, negative-binomial |\n\n    Accordingly, one can use the [variance-to-mean ratio][variance-to-mean-ratio] to assess whether observed data can be modeled as a Poisson process. When observed data is \"under-dispersed\", observed data may be more regular than as would be the case for a Poisson process. When observed data is \"over-dispersed\", observed data may contain clusters (i.e., clumped, concentrated data).\n\n-   The [variance-to-mean ratio][variance-to-mean-ratio] is typically computed on nonnegative values. The measure may lack meaning for data which can assume both positive and negative values.\n\n-   The [variance-to-mean ratio][variance-to-mean-ratio] is also known as the **index of dispersion**, **dispersion index**, **coefficient of dispersion**, **relative variance**, and the [**Fano factor**][fano-factor].\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 incrmvmr = require( '@stdlib/stats-incr-mvmr' );\n\nvar accumulator;\nvar v;\nvar i;\n\n// Initialize an accumulator:\naccumulator = incrmvmr( 5 );\n\n// For each simulated datum, update the moving variance-to-mean ratio...\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\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/mmean`][@stdlib/stats/incr/mmean]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecompute a moving arithmetic mean incrementally.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-incr/mvariance`][@stdlib/stats/incr/mvariance]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecompute a moving unbiased sample variance incrementally.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-incr/vmr`][@stdlib/stats/incr/vmr]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecompute a variance-to-mean ratio (VMR) 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-mvmr.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-incr-mvmr\n\n[test-image]: https://github.com/stdlib-js/stats-incr-mvmr/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/stats-incr-mvmr/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-incr-mvmr/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-incr-mvmr?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-incr-mvmr.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-incr-mvmr/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-mvmr/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-incr-mvmr/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-incr-mvmr/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-incr-mvmr/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-incr-mvmr/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-incr-mvmr/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-incr-mvmr/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-mvmr/main/LICENSE\n\n[variance-to-mean-ratio]: https://en.wikipedia.org/wiki/Index_of_dispersion\n\n[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean\n\n[sample-variance]: https://en.wikipedia.org/wiki/Variance\n\n[fano-factor]: https://en.wikipedia.org/wiki/Fano_factor\n\n\u003c!-- \u003crelated-links\u003e --\u003e\n\n[@stdlib/stats/incr/mmean]: https://github.com/stdlib-js/stats-incr-mmean\n\n[@stdlib/stats/incr/mvariance]: https://github.com/stdlib-js/stats-incr-mvariance\n\n[@stdlib/stats/incr/vmr]: https://github.com/stdlib-js/stats-incr-vmr\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-mvmr","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fstats-incr-mvmr","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-incr-mvmr/lists"}