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\n \n About stdlib...\n \n

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.

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\n
\n\n# variancepn\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \n\n> Calculate the [variance][variance] of a strided array using a two-pass algorithm.\n\n
\n\nThe population [variance][variance] of a finite size population of size `N` is given by\n\n\n\n
\n \"Equation\n
\n
-->\n\n\n\nwhere the population mean is given by\n\n\n\n\n\n\n\nOften in the analysis of data, the true population [variance][variance] 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 [variance][variance], the result is biased and yields a **biased sample variance**. To compute an **unbiased sample variance** for a sample of size `n`,\n\n\n\n\n\n\n\nwhere the sample mean is given by\n\n\n\n\n\nThe 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 variance and population variance. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.\n\n
\n\n\n\n
\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-strided-variancepn\n```\n\n
\n\n
\n\n## Usage\n\n```javascript\nvar variancepn = require( '@stdlib/stats-strided-variancepn' );\n```\n\n#### variancepn( N, correction, x, strideX )\n\nComputes the [variance][variance] of a strided array using a two-pass algorithm.\n\n```javascript\nvar x = [ 1.0, -2.0, 2.0 ];\n\nvar v = variancepn( x.length, 1, x, 1 );\n// returns ~4.3333\n```\n\nThe function has the following parameters:\n\n- **N**: number of indexed elements.\n- **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 [variance][variance] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [variance][variance] 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 [variance][variance], 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).\n- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].\n- **strideX**: stride length for `x`.\n\nThe `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [variance][variance] of every other element in `x`,\n\n```javascript\nvar x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];\n\nvar v = variancepn( 4, 1, x, 2 );\n// returns 6.25\n```\n\nNote that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.\n\n\n\n```javascript\nvar Float64Array = require( '@stdlib/array-float64' );\n\nvar x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );\nvar x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element\n\nvar v = variancepn( 4, 1, x1, 2 );\n// returns 6.25\n```\n\n#### variancepn.ndarray( N, correction, x, strideX, offsetX )\n\nComputes the [variance][variance] of a strided array using a two-pass algorithm and alternative indexing semantics.\n\n```javascript\nvar x = [ 1.0, -2.0, 2.0 ];\n\nvar v = variancepn.ndarray( x.length, 1, x, 1, 0 );\n// returns ~4.33333\n```\n\nThe function has the following additional parameters:\n\n- **offsetX**: starting index for `x`.\n\nWhile [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to calculate the [variance][variance] for every other element in `x` starting from the second element\n\n```javascript\nvar x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];\n\nvar v = variancepn.ndarray( 4, 1, x, 2, 1 );\n// returns 6.25\n```\n\n
\n\n\n\n
\n\n## Notes\n\n- If `N <= 0`, both functions return `NaN`.\n- If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), both functions return `NaN`.\n- Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array-base/accessor`][@stdlib/array/base/accessor]).\n- Depending on the environment, the typed versions ([`dvariancepn`][@stdlib/stats/strided/dvariancepn], [`svariancepn`][@stdlib/stats/strided/svariancepn], etc.) are likely to be significantly more performant.\n\n
\n\n\n\n
\n\n## Examples\n\n\n\n```javascript\nvar discreteUniform = require( '@stdlib/random-array-discrete-uniform' );\nvar variancepn = require( '@stdlib/stats-strided-variancepn' );\n\nvar x = discreteUniform( 10, -50, 50, {\n 'dtype': 'float64'\n});\nconsole.log( x );\n\nvar v = variancepn( x.length, 1, x, 1 );\nconsole.log( v );\n```\n\n
\n\n\n\n* * *\n\n
\n\n## References\n\n- Neely, Peter M. 1966. \"Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients.\" _Communications of the ACM_ 9 (7). Association for Computing Machinery: 496–99. doi:[10.1145/365719.365958][@neely:1966a].\n- Schubert, Erich, and Michael Gertz. 2018. \"Numerically Stable Parallel Computation of (Co-)Variance.\" In _Proceedings of the 30th International Conference on Scientific and Statistical Database Management_. New York, NY, USA: Association for Computing Machinery. doi:[10.1145/3221269.3223036][@schubert:2018a].\n\n
\n\n\n\n\n\n
\n\n* * *\n\n## See Also\n\n- [`@stdlib/stats-strided/dvariancepn`][@stdlib/stats/strided/dvariancepn]: calculate the variance of a double-precision floating-point strided array using a two-pass algorithm.\n- [`@stdlib/stats-strided/nanvariancepn`][@stdlib/stats/strided/nanvariancepn]: calculate the variance of a strided array ignoring NaN values and using a two-pass algorithm.\n- [`@stdlib/stats-strided/stdevpn`][@stdlib/stats/strided/stdevpn]: calculate the standard deviation of a strided array using a two-pass algorithm.\n- [`@stdlib/stats-strided/variance`][@stdlib/stats/strided/variance]: calculate the variance of a strided array.\n\n
\n\n\n\n\n\n\n
\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 © 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n
\n\n\n\n\n\n
\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-strided-variancepn.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-strided-variancepn\n\n[test-image]: https://github.com/stdlib-js/stats-strided-variancepn/actions/workflows/test.yml/badge.svg?branch=v0.1.1\n[test-url]: https://github.com/stdlib-js/stats-strided-variancepn/actions/workflows/test.yml?query=branch:v0.1.1\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-strided-variancepn/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-strided-variancepn?branch=main\n\n\n\n[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-url]: https://stdlib.zulipchat.com\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-strided-variancepn/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-strided-variancepn/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-strided-variancepn/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-strided-variancepn/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-strided-variancepn/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-strided-variancepn/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-strided-variancepn/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-strided-variancepn/main/LICENSE\n\n[variance]: https://en.wikipedia.org/wiki/Variance\n\n[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array\n\n[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray\n\n[@stdlib/stats/strided/svariancepn]: https://www.npmjs.com/package/@stdlib/stats-strided-svariancepn\n\n[@neely:1966a]: https://doi.org/10.1145/365719.365958\n\n[@schubert:2018a]: https://doi.org/10.1145/3221269.3223036\n\n[@stdlib/array/base/accessor]: https://www.npmjs.com/package/@stdlib/array-base-accessor\n\n\n\n[@stdlib/stats/strided/dvariancepn]: https://www.npmjs.com/package/@stdlib/stats-strided-dvariancepn\n\n[@stdlib/stats/strided/nanvariancepn]: https://www.npmjs.com/package/@stdlib/stats-strided-nanvariancepn\n\n[@stdlib/stats/strided/stdevpn]: https://www.npmjs.com/package/@stdlib/stats-strided-stdevpn\n\n[@stdlib/stats/strided/variance]: https://www.npmjs.com/package/@stdlib/stats-strided-variance\n\n\n\n
\n\n\n","readmeFilename":"README.md"}