160 lines
6.3 KiB
Markdown
160 lines
6.3 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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# Student's T
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> Student's t distribution.
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<section class="usage">
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## Usage
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```javascript
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var t = require( '@stdlib/stats/base/dists/t' );
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```
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#### t
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Student's t distribution.
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```javascript
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var dist = t;
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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, v )`][@stdlib/stats/base/dists/t/cdf]</span><span class="delimiter">: </span><span class="description">Student's t distribution cumulative distribution function (CDF).</span>
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- <span class="signature">[`logcdf( x, v )`][@stdlib/stats/base/dists/t/logcdf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the cumulative distribution function (CDF) for a Student's t distribution.</span>
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- <span class="signature">[`logpdf( x, v )`][@stdlib/stats/base/dists/t/logpdf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the probability density function (PDF) for a Student's t distribution.</span>
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- <span class="signature">[`pdf( x, v )`][@stdlib/stats/base/dists/t/pdf]</span><span class="delimiter">: </span><span class="description">Student's t distribution probability density function (PDF).</span>
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- <span class="signature">[`quantile( p, v )`][@stdlib/stats/base/dists/t/quantile]</span><span class="delimiter">: </span><span class="description">Student's t 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( v )`][@stdlib/stats/base/dists/t/entropy]</span><span class="delimiter">: </span><span class="description">Student's t distribution differential entropy.</span>
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- <span class="signature">[`kurtosis( v )`][@stdlib/stats/base/dists/t/kurtosis]</span><span class="delimiter">: </span><span class="description">Student's t distribution excess kurtosis.</span>
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- <span class="signature">[`mean( v )`][@stdlib/stats/base/dists/t/mean]</span><span class="delimiter">: </span><span class="description">Student's t distribution expected value.</span>
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- <span class="signature">[`median( v )`][@stdlib/stats/base/dists/t/median]</span><span class="delimiter">: </span><span class="description">Student's t distribution median.</span>
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- <span class="signature">[`mode( v )`][@stdlib/stats/base/dists/t/mode]</span><span class="delimiter">: </span><span class="description">Student's t distribution mode.</span>
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- <span class="signature">[`skewness( v )`][@stdlib/stats/base/dists/t/skewness]</span><span class="delimiter">: </span><span class="description">Student's t distribution skewness.</span>
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- <span class="signature">[`stdev( v )`][@stdlib/stats/base/dists/t/stdev]</span><span class="delimiter">: </span><span class="description">Student's t distribution variance.</span>
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- <span class="signature">[`variance( v )`][@stdlib/stats/base/dists/t/variance]</span><span class="delimiter">: </span><span class="description">Student's t 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 [Student's t][t-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">[`T( [v] )`][@stdlib/stats/base/dists/t/ctor]</span><span class="delimiter">: </span><span class="description">Student's t distribution constructor.</span>
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</div>
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<!-- </toc> -->
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```javascript
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var T = require( '@stdlib/stats/base/dists/t' ).T;
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var dist = new T( 2.0 );
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var y = dist.cdf( 0.5 );
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// returns ~0.667
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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 t = require( '@stdlib/stats/base/dists/t' );
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console.log( objectKeys( t ) );
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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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[t-distribution]: https://en.wikipedia.org/wiki/Student%27s_t-distribution
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<!-- <toc-links> -->
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[@stdlib/stats/base/dists/t/ctor]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/ctor
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[@stdlib/stats/base/dists/t/entropy]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/entropy
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[@stdlib/stats/base/dists/t/kurtosis]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/kurtosis
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[@stdlib/stats/base/dists/t/mean]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/mean
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[@stdlib/stats/base/dists/t/median]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/median
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[@stdlib/stats/base/dists/t/mode]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/mode
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[@stdlib/stats/base/dists/t/skewness]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/skewness
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[@stdlib/stats/base/dists/t/stdev]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/stdev
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[@stdlib/stats/base/dists/t/variance]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/variance
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[@stdlib/stats/base/dists/t/cdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/cdf
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[@stdlib/stats/base/dists/t/logcdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/logcdf
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[@stdlib/stats/base/dists/t/logpdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/logpdf
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[@stdlib/stats/base/dists/t/pdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/pdf
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[@stdlib/stats/base/dists/t/quantile]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/t/quantile
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<!-- </toc-links> -->
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</section>
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<!-- /.links -->
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