145 lines
5.0 KiB
Markdown
145 lines
5.0 KiB
Markdown
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Cauchy
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> Cauchy distribution.
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<section class="usage">
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## Usage
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```javascript
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var cauchy = require( '@stdlib/stats/base/dists/cauchy' );
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```
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#### cauchy
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Cauchy distribution.
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```javascript
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var dist = cauchy;
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// returns {...}
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```
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The namespace contains the following distribution functions:
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<!-- <toc pattern="*+(cdf|pdf|mgf|quantile)*"> -->
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<div class="namespace-toc">
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- <span class="signature">[`cdf( x, x0, gamma )`][@stdlib/stats/base/dists/cauchy/cdf]</span><span class="delimiter">: </span><span class="description">Cauchy distribution cumulative distribution function.</span>
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- <span class="signature">[`logcdf( x, x0, gamma )`][@stdlib/stats/base/dists/cauchy/logcdf]</span><span class="delimiter">: </span><span class="description">Cauchy distribution logarithm of cumulative distribution function.</span>
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- <span class="signature">[`logpdf( x, x0, gamma )`][@stdlib/stats/base/dists/cauchy/logpdf]</span><span class="delimiter">: </span><span class="description">Cauchy distribution logarithm of probability density function (logPDF).</span>
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- <span class="signature">[`pdf( x, x0, gamma )`][@stdlib/stats/base/dists/cauchy/pdf]</span><span class="delimiter">: </span><span class="description">Cauchy distribution probability density function (PDF).</span>
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- <span class="signature">[`quantile( p, x0, gamma )`][@stdlib/stats/base/dists/cauchy/quantile]</span><span class="delimiter">: </span><span class="description">Cauchy distribution quantile function.</span>
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</div>
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<!-- </toc> -->
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The namespace contains the following functions for calculating distribution properties:
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<!-- <toc pattern="*+(entropy|kurtosis|mean|median|mode|skewness|stdev|variance)*"> -->
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<div class="namespace-toc">
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- <span class="signature">[`entropy( x0, gamma )`][@stdlib/stats/base/dists/cauchy/entropy]</span><span class="delimiter">: </span><span class="description">Cauchy distribution differential entropy.</span>
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- <span class="signature">[`median( x0, gamma )`][@stdlib/stats/base/dists/cauchy/median]</span><span class="delimiter">: </span><span class="description">Cauchy distribution median.</span>
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- <span class="signature">[`mode( x0, gamma )`][@stdlib/stats/base/dists/cauchy/mode]</span><span class="delimiter">: </span><span class="description">Cauchy distribution mode.</span>
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</div>
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<!-- </toc> -->
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The namespace contains a constructor function for creating a [Cauchy][cauchy-distribution] distribution object.
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<!-- <toc pattern="*ctor*"> -->
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<div class="namespace-toc">
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- <span class="signature">[`Cauchy( [x0, gamma] )`][@stdlib/stats/base/dists/cauchy/ctor]</span><span class="delimiter">: </span><span class="description">Cauchy distribution constructor.</span>
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</div>
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<!-- </toc> -->
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```javascript
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var Cauchy = require( '@stdlib/stats/base/dists/cauchy' ).Cauchy;
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var dist = new Cauchy( 2.0, 4.0 );
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var median = dist.median;
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// returns 2.0
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- TODO: better examples -->
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<!-- eslint no-undef: "error" -->
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```javascript
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var objectKeys = require( '@stdlib/utils/keys' );
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var cauchy = require( '@stdlib/stats/base/dists/cauchy' );
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console.log( objectKeys( cauchy ) );
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[cauchy-distribution]: https://en.wikipedia.org/wiki/Cauchy_distribution
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<!-- <toc-links> -->
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[@stdlib/stats/base/dists/cauchy/ctor]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/cauchy/ctor
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[@stdlib/stats/base/dists/cauchy/entropy]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/cauchy/entropy
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[@stdlib/stats/base/dists/cauchy/median]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/cauchy/median
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[@stdlib/stats/base/dists/cauchy/mode]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/cauchy/mode
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[@stdlib/stats/base/dists/cauchy/cdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/cauchy/cdf
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[@stdlib/stats/base/dists/cauchy/logcdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/cauchy/logcdf
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[@stdlib/stats/base/dists/cauchy/logpdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/cauchy/logpdf
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[@stdlib/stats/base/dists/cauchy/pdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/cauchy/pdf
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[@stdlib/stats/base/dists/cauchy/quantile]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/cauchy/quantile
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<!-- </toc-links> -->
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</section>
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<!-- /.links -->
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