@stdlib/stats-kstest

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We greatly appreciate your continued support!</p> </details> # Kolmogorov-Smirnov Goodness-of-Fit Test [![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]  > One-sample Kolmogorov-Smirnov goodness-of-fit test. <section class="installation"> ## Installation ```bash npm install @stdlib/stats-kstest ``` </section> <section class="usage"> ## Usage ```javascript var kstest = require( '@stdlib/stats-kstest' ); ``` #### kstest( x, y\[, ...params]\[, opts] ) For a numeric [array][mdn-array] or [typed array][mdn-typed-array] `x`, a Kolmogorov-Smirnov goodness-of-fit is computed for the null hypothesis that the values of `x` come from the distribution specified by `y`. `y` can be either a [string][mdn-string] with the name of the distribution to test against, or a [function][mdn-function]. In the latter case, `y` is expected to be the cumulative distribution function (CDF) of the distribution to test against, with its first parameter being the value at which to evaluate the CDF and the remaining parameters constituting the parameters of the distribution. The parameters of the distribution are passed as additional arguments after `y` from `kstest` to the chosen CDF. The function returns an object holding the calculated test statistic `statistic` and the `pValue` of the test. ```javascript var factory = require( '@stdlib/random-base-uniform' ).factory; var runif; var out; var x; var i; runif = factory( 0.0, 1.0, { 'seed': 8798 }); x = new Array( 100 ); for ( i = 0; i < x.length; i++ ) { x[ i ] = runif(); } out = kstest( x, 'uniform', 0.0, 1.0 ); // returns { 'pValue': ~0.703, 'statistic': ~0.069, ... } ``` The returned object comes with a `.print()` method which when invoked will print a formatted output of the hypothesis test results. `print` accepts a `digits` option that controls the number of decimal digits displayed for the outputs and a `decision` option, which when set to `false` will hide the test decision.  ```javascript console.log( out.print() ); /* e.g., => Kolmogorov-Smirnov goodness-of-fit test. Null hypothesis: the CDF of `x` is equal equal to the reference CDF. pValue: 0.7039 statistic: 0.0689 Test Decision: Fail to reject null in favor of alternative at 5% significance level */ ``` The function accepts the following `options`: - **alpha**: `number` in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`. - **alternative**: Either `two-sided`, `less` or `greater`. Indicates whether the alternative hypothesis is that the true distribution of `x` is not equal to the reference distribution specified by `y` (`two-sided`), whether it is `less` than the reference distribution or `greater` than the reference distribution. Default: `two-sided`. - **sorted**: `boolean` indicating if the `x` [array][mdn-array] is in sorted order (ascending). Default: `false`. By default, the test is carried out at a significance level of `0.05`. To choose a custom significance level, set the `alpha` option.  ```javascript out = kstest( x, 'uniform', 0.0, 1.0, { 'alpha': 0.1 }); console.log( out.print() ); /* e.g., => Kolmogorov-Smirnov goodness-of-fit test. Null hypothesis: the CDF of `x` is equal equal to the reference CDF. pValue: 0.7039 statistic: 0.0689 Test Decision: Fail to reject null in favor of alternative at 10% significance level */ ``` By default, the function tests the null hypothesis that the true distribution of `x` and the reference distribution `y` are equal to each other against the alternative that they are not equal. To carry out a one-sided hypothesis test, set the `alternative` option to either `less` or `greater`. ```javascript var factory = require( '@stdlib/random-base-uniform' ).factory; var runif; var out; var x; var i; runif = factory( 0.0, 1.0, { 'seed': 8798 }); x = new Array( 100 ); for ( i = 0; i < x.length; i++ ) { x[ i ] = runif(); } out = kstest( x, 'uniform', 0.0, 1.0, { 'alternative': 'less' }); // returns { 'pValue': ~0.358, 'statistic': ~0.07, ... } out = kstest( x, 'uniform', 0.0, 1.0, { 'alternative': 'greater' }); // returns { 'pValue': ~0.907, 'statistic': ~0.02, ... } ``` To perform the Kolmogorov-Smirnov test, the data has to be sorted in ascending order. If the data in `x` are already sorted, set the `sorted` option to `true` to speed up computation. ```javascript x = [ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 ]; out = kstest( x, 'uniform', 0.0, 1.0, { 'sorted': true }); // returns { 'pValue': ~1, 'statistic': 0.1, ... } ``` </section>  <section class="examples"> ## Examples  ```javascript var kstest = require( '@stdlib/stats-kstest' ); var factory = require( '@stdlib/random-base-normal' ).factory; var rnorm; var table; var out; var i; var x; rnorm = factory({ 'seed': 4839 }); // Values drawn from a Normal(3,1) distribution x = new Array( 100 ); for ( i = 0; i < 100; i++ ) { x[ i ] = rnorm( 3.0, 1.0 ); } // Test against N(0,1) out = kstest( x, 'normal', 0.0, 1.0 ); table = out.print(); /* e.g., returns Kolmogorov-Smirnov goodness-of-fit test. Null hypothesis: the CDF of `x` is equal to the reference CDF. statistic: 0.847 pValue: 0 Test Decision: Reject null in favor of alternative at 5% significance level */ // Test against N(3,1) out = kstest( x, 'normal', 3.0, 1.0 ); table = out.print(); /* e.g., returns Kolmogorov-Smirnov goodness-of-fit test. Null hypothesis: the CDF of `x` is equal to the reference CDF. statistic: 0.0733 pValue: 0.6282 Test Decision: Fail to reject null in favor of alternative at 5% significance level */ ``` </section>   <section class="related"> </section>   <section class="main-repo" > * * * ## 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 © 2016-2026. The Stdlib [Authors][stdlib-authors]. </section>   <section class="links"> [npm-image]: http://img.shields.io/npm/v/@stdlib/stats-kstest.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-kstest [test-image]: https://github.com/stdlib-js/stats-kstest/actions/workflows/test.yml/badge.svg?branch=v0.2.3 [test-url]: https://github.com/stdlib-js/stats-kstest/actions/workflows/test.yml?query=branch:v0.2.3 [coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-kstest/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/stats-kstest?branch=main  [chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com [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-kstest/tree/deno [deno-readme]: https://github.com/stdlib-js/stats-kstest/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/stats-kstest/tree/umd [umd-readme]: https://github.com/stdlib-js/stats-kstest/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/stats-kstest/tree/esm [esm-readme]: https://github.com/stdlib-js/stats-kstest/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/stats-kstest/blob/main/branches.md [stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-kstest/main/LICENSE [mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array [mdn-function]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Function [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays [mdn-string]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/String </section>