162 lines
6.8 KiB
Markdown
162 lines
6.8 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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# Beta
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> Beta distribution.
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<section class="usage">
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## Usage
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```javascript
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var beta = require( '@stdlib/stats/base/dists/beta' );
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```
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#### beta
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[Beta][beta-distribution] distribution.
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```javascript
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var dist = beta;
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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, alpha, beta )`][@stdlib/stats/base/dists/beta/cdf]</span><span class="delimiter">: </span><span class="description">beta distribution cumulative distribution function.</span>
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- <span class="signature">[`logcdf( x, alpha, beta )`][@stdlib/stats/base/dists/beta/logcdf]</span><span class="delimiter">: </span><span class="description">beta distribution logarithm of cumulative distribution function.</span>
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- <span class="signature">[`logpdf( x, alpha, beta )`][@stdlib/stats/base/dists/beta/logpdf]</span><span class="delimiter">: </span><span class="description">beta distribution logarithm of probability density function (PDF).</span>
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- <span class="signature">[`mgf( t, alpha, beta )`][@stdlib/stats/base/dists/beta/mgf]</span><span class="delimiter">: </span><span class="description">beta distribution moment-generating function (MGF).</span>
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- <span class="signature">[`pdf( x, alpha, beta )`][@stdlib/stats/base/dists/beta/pdf]</span><span class="delimiter">: </span><span class="description">beta distribution probability density function (PDF).</span>
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- <span class="signature">[`quantile( p, alpha, beta )`][@stdlib/stats/base/dists/beta/quantile]</span><span class="delimiter">: </span><span class="description">beta 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( alpha, beta )`][@stdlib/stats/base/dists/beta/entropy]</span><span class="delimiter">: </span><span class="description">beta distribution differential entropy.</span>
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- <span class="signature">[`kurtosis( alpha, beta )`][@stdlib/stats/base/dists/beta/kurtosis]</span><span class="delimiter">: </span><span class="description">beta distribution excess kurtosis.</span>
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- <span class="signature">[`mean( alpha, beta )`][@stdlib/stats/base/dists/beta/mean]</span><span class="delimiter">: </span><span class="description">beta distribution expected value.</span>
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- <span class="signature">[`median( alpha, beta )`][@stdlib/stats/base/dists/beta/median]</span><span class="delimiter">: </span><span class="description">beta distribution median.</span>
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- <span class="signature">[`mode( alpha, beta )`][@stdlib/stats/base/dists/beta/mode]</span><span class="delimiter">: </span><span class="description">beta distribution mode.</span>
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- <span class="signature">[`skewness( alpha, beta )`][@stdlib/stats/base/dists/beta/skewness]</span><span class="delimiter">: </span><span class="description">beta distribution skewness.</span>
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- <span class="signature">[`stdev( alpha, beta )`][@stdlib/stats/base/dists/beta/stdev]</span><span class="delimiter">: </span><span class="description">beta distribution standard deviation.</span>
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- <span class="signature">[`variance( alpha, beta )`][@stdlib/stats/base/dists/beta/variance]</span><span class="delimiter">: </span><span class="description">beta distribution variance.</span>
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</div>
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<!-- </toc> -->
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The namespace contains a constructor function for creating a [beta][beta-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">[`Beta( [alpha, beta] )`][@stdlib/stats/base/dists/beta/ctor]</span><span class="delimiter">: </span><span class="description">beta distribution constructor.</span>
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</div>
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<!-- </toc> -->
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```javascript
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var Beta = require( '@stdlib/stats/base/dists/beta' ).Beta;
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var dist = new Beta( 2.0, 4.0 );
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var mu = dist.mean;
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// returns ~0.333
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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 beta = require( '@stdlib/stats/base/dists/beta' );
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console.log( objectKeys( beta ) );
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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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[beta-distribution]: https://en.wikipedia.org/wiki/Beta_distribution
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<!-- <toc-links> -->
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[@stdlib/stats/base/dists/beta/ctor]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/ctor
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[@stdlib/stats/base/dists/beta/entropy]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/entropy
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[@stdlib/stats/base/dists/beta/kurtosis]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/kurtosis
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[@stdlib/stats/base/dists/beta/mean]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/mean
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[@stdlib/stats/base/dists/beta/median]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/median
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[@stdlib/stats/base/dists/beta/mode]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/mode
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[@stdlib/stats/base/dists/beta/skewness]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/skewness
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[@stdlib/stats/base/dists/beta/stdev]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/stdev
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[@stdlib/stats/base/dists/beta/variance]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/variance
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[@stdlib/stats/base/dists/beta/cdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/cdf
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[@stdlib/stats/base/dists/beta/logcdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/logcdf
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[@stdlib/stats/base/dists/beta/logpdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/logpdf
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[@stdlib/stats/base/dists/beta/mgf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/mgf
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[@stdlib/stats/base/dists/beta/pdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/pdf
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[@stdlib/stats/base/dists/beta/quantile]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/quantile
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<!-- </toc-links> -->
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</section>
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<!-- /.links -->
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