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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# Poisson
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> Poisson distribution.
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<section class="usage">
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## Usage
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```javascript
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var poisson = require( '@stdlib/stats/base/dists/poisson' );
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```
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#### poisson
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Poisson distribution.
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```javascript
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var dist = poisson;
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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|pmf|mgf|quantile)*"> -->
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<div class="namespace-toc">
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- <span class="signature">[`cdf( x, lambda )`][@stdlib/stats/base/dists/poisson/cdf]</span><span class="delimiter">: </span><span class="description">Poisson distribution cumulative distribution function.</span>
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- <span class="signature">[`logpmf( x, lambda )`][@stdlib/stats/base/dists/poisson/logpmf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the probability mass function (PMF) for a Poisson distribution.</span>
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- <span class="signature">[`mgf( t, lambda )`][@stdlib/stats/base/dists/poisson/mgf]</span><span class="delimiter">: </span><span class="description">Poisson distribution moment-generating function (MGF).</span>
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- <span class="signature">[`pmf( x, lambda )`][@stdlib/stats/base/dists/poisson/pmf]</span><span class="delimiter">: </span><span class="description">Poisson distribution probability mass function (PMF).</span>
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- <span class="signature">[`quantile( p, lambda )`][@stdlib/stats/base/dists/poisson/quantile]</span><span class="delimiter">: </span><span class="description">Poisson 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">[`kurtosis( lambda )`][@stdlib/stats/base/dists/poisson/kurtosis]</span><span class="delimiter">: </span><span class="description">Poisson distribution excess kurtosis.</span>
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- <span class="signature">[`mean( lambda )`][@stdlib/stats/base/dists/poisson/mean]</span><span class="delimiter">: </span><span class="description">Poisson distribution expected value.</span>
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- <span class="signature">[`median( lambda )`][@stdlib/stats/base/dists/poisson/median]</span><span class="delimiter">: </span><span class="description">Poisson distribution median.</span>
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- <span class="signature">[`mode( lambda )`][@stdlib/stats/base/dists/poisson/mode]</span><span class="delimiter">: </span><span class="description">Poisson distribution mode.</span>
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- <span class="signature">[`skewness( lambda )`][@stdlib/stats/base/dists/poisson/skewness]</span><span class="delimiter">: </span><span class="description">Poisson distribution skewness.</span>
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- <span class="signature">[`stdev( lambda )`][@stdlib/stats/base/dists/poisson/stdev]</span><span class="delimiter">: </span><span class="description">Poisson distribution standard deviation.</span>
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- <span class="signature">[`variance( lambda )`][@stdlib/stats/base/dists/poisson/variance]</span><span class="delimiter">: </span><span class="description">Poisson 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 [Poisson][poisson-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">[`Poisson( [lambda] )`][@stdlib/stats/base/dists/poisson/ctor]</span><span class="delimiter">: </span><span class="description">Poisson distribution constructor.</span>
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</div>
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<!-- </toc> -->
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```javascript
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var Poisson = require( '@stdlib/stats/base/dists/poisson' ).Poisson;
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var dist = new Poisson( 2.0 );
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var y = dist.pmf( 3.0 );
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// returns ~0.18
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y = dist.pmf( 2.3 );
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// returns 0.0
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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 poisson = require( '@stdlib/stats/base/dists/poisson' );
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console.log( objectKeys( poisson ) );
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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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[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution
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<!-- <toc-links> -->
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[@stdlib/stats/base/dists/poisson/ctor]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/ctor
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[@stdlib/stats/base/dists/poisson/kurtosis]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/kurtosis
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[@stdlib/stats/base/dists/poisson/mean]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/mean
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[@stdlib/stats/base/dists/poisson/median]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/median
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[@stdlib/stats/base/dists/poisson/mode]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/mode
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[@stdlib/stats/base/dists/poisson/skewness]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/skewness
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[@stdlib/stats/base/dists/poisson/stdev]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/stdev
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[@stdlib/stats/base/dists/poisson/variance]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/variance
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[@stdlib/stats/base/dists/poisson/cdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/cdf
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[@stdlib/stats/base/dists/poisson/logpmf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/logpmf
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[@stdlib/stats/base/dists/poisson/mgf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/mgf
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[@stdlib/stats/base/dists/poisson/pmf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/pmf
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[@stdlib/stats/base/dists/poisson/quantile]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/poisson/quantile
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<!-- </toc-links> -->
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</section>
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<!-- /.links -->
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