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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# Probability Density Function\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 [Degenerate distribution][degenerate-distribution] [probability density function][pdf] (PDF).\n\n\u003csection class=\"intro\"\u003e\n\nStrictly speaking, as a discrete distribution, a [degenerate][degenerate-distribution] has no [probability density function][pdf] (PDF). Extending the notion of a [PDF][pdf], we conceptualize the [PDF][pdf] of a [degenerate][degenerate-distribution] as an infinitely tall spike centered at `mu`. More formally,\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:degenerate_pdf\" align=\"center\" raw=\"f(x;\\mu) = \\delta(x-\\mu)\" alt=\"Probability density function (PDF) for a degenerate distribution.\"\u003e --\u003e\n\n```math\nf(x;\\mu) = \\delta(x-\\mu)\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"f(x;\\mu) = \\delta(x-\\mu)\" data-equation=\"eq:degenerate_pdf\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/degenerate/pdf/docs/img/equation_degenerate_pdf.svg\" alt=\"Probability density function (PDF) for a degenerate distribution.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere `delta` is the Dirac delta function.\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:dirac_delta\" align=\"center\" raw=\"\\delta(x) = {\\begin{cases}+\\infty, \u0026 x = 0\\\\0, \u0026 x \\neq 0\\end{cases}}\" alt=\"Dirac delta function.\"\u003e --\u003e\n\n```math\n\\delta(x) = {\\begin{cases}+\\infty, \u0026 x = 0\\\\0, \u0026 x \\neq 0\\end{cases}}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"\\delta(x) = {\\begin{cases}+\\infty, \u0026amp; x = 0\\\\0, \u0026amp; x \\neq 0\\end{cases}}\" data-equation=\"eq:dirac_delta\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/degenerate/pdf/docs/img/equation_dirac_delta.svg\" alt=\"Dirac delta function.\"\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-base-dists-degenerate-pdf\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 pdf = require( '@stdlib/stats-base-dists-degenerate-pdf' );\n```\n\n#### pdf( x, mu )\n\nEvaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.\n\n```javascript\nvar y = pdf( 2.0, 8.0 );\n// returns 0.0\n\ny = pdf( 8.0, 8.0 );\n// returns Infinity\n```\n\n#### pdf.factory( mu )\n\nReturns a function for evaluating the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.\n\n```javascript\nvar mypdf = pdf.factory( 10.0 );\n\nvar y = mypdf( 10.0 );\n// returns Infinity\n\ny = mypdf( 5.0 );\n// returns 0.0\n\ny = mypdf( 12.0 );\n// returns 0.0\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar pdf = require( '@stdlib/stats-base-dists-degenerate-pdf' );\nvar discreteUniform = require( '@stdlib/random-array-discrete-uniform' );\nvar logEachMap = require( '@stdlib/console-log-each-map' );\n\nvar opts = {\n    'dtype': 'float64'\n};\nvar x = discreteUniform( 100, 0, 5, opts );\nvar mu = discreteUniform( 100, 0, 5, opts );\n\nlogEachMap( 'x: %0.4f, µ: %0.4f, f(x;µ): %0.4f', x, mu, pdf );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c!-- C interface documentation. --\u003e\n\n* * *\n\n\u003csection class=\"c\"\u003e\n\n## C APIs\n\n\u003c!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"intro\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003c!-- C usage documentation. --\u003e\n\n\u003csection class=\"usage\"\u003e\n\n### Usage\n\n```c\n#include \"stdlib/stats/base/dists/degenerate/pdf.h\"\n```\n\n#### stdlib_base_dists_degenerate_pdf( x, mu )\n\nEvaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.\n\n```c\ndouble out = stdlib_base_dists_degenerate_pdf( 2.0, 3.0 );\n// returns 0.0\n```\n\nThe function accepts the following arguments:\n\n-   **x**: `[in] double` input value.\n-   **mu**: `[in] double` constant value of the distribution.\n\n```c\ndouble stdlib_base_dists_degenerate_pdf( const double x, const double mu );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003c!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"notes\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.notes --\u003e\n\n\u003c!-- C API usage examples. --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n### Examples\n\n```c\n#include \"stdlib/stats/base/dists/degenerate/pdf.h\"\n#include \"stdlib/math/base/special/round.h\"\n#include \u003cstdlib.h\u003e\n#include \u003cstdio.h\u003e\n\nstatic double random_uniform( const double min, const double max ) {\n    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );\n    return min + ( v * ( max - min ) );\n}\n\nint main( void ) {\n    double result;\n    double mu;\n    double x;\n    int i;\n\n    for ( i = 0; i \u003c 10; i++ ) {\n        x = stdlib_base_round( random_uniform( 0.0, 5.0 ) );\n        mu = stdlib_base_round( random_uniform( 0.0, 5.0 ) );\n        result = stdlib_base_dists_degenerate_pdf( x, mu );\n        printf( \"x: %lf, µ: %lf, f(x;µ): %lf \\n\", x, mu, result );\n    }\n}\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.c --\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\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-base-dists-degenerate-pdf.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-degenerate-pdf\n\n[test-image]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-degenerate-pdf/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-degenerate-pdf?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-base-dists-degenerate-pdf.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-base-dists-degenerate-pdf/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-base-dists-degenerate-pdf/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-degenerate-pdf/main/LICENSE\n\n[pdf]: https://en.wikipedia.org/wiki/Probability_density_function\n\n[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution\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-base-dists-degenerate-pdf","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fstats-base-dists-degenerate-pdf","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-base-dists-degenerate-pdf/lists"}