154 lines
6.6 KiB
Markdown
154 lines
6.6 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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# Negative Binomial
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> Negative binomial distribution.
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<section class="usage">
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## Usage
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```javascript
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var negativeBinomial = require( '@stdlib/stats/base/dists/negative-binomial' );
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```
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#### negativeBinomial
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Negative binomial distribution.
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```javascript
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var dist = negativeBinomial;
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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, r, p )`][@stdlib/stats/base/dists/negative-binomial/cdf]</span><span class="delimiter">: </span><span class="description">negative binomial distribution cumulative distribution function.</span>
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- <span class="signature">[`logpmf( x, r, p )`][@stdlib/stats/base/dists/negative-binomial/logpmf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the probability mass function (PMF) for a negative binomial distribution.</span>
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- <span class="signature">[`mgf( t, r, p )`][@stdlib/stats/base/dists/negative-binomial/mgf]</span><span class="delimiter">: </span><span class="description">negative binomial distribution moment-generating function (MGF).</span>
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- <span class="signature">[`pmf( x, r, p )`][@stdlib/stats/base/dists/negative-binomial/pmf]</span><span class="delimiter">: </span><span class="description">negative binomial distribution probability mass function (PMF).</span>
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- <span class="signature">[`quantile( k, r, p )`][@stdlib/stats/base/dists/negative-binomial/quantile]</span><span class="delimiter">: </span><span class="description">negative binomial 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( r, p )`][@stdlib/stats/base/dists/negative-binomial/kurtosis]</span><span class="delimiter">: </span><span class="description">negative binomial distribution excess kurtosis.</span>
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- <span class="signature">[`mean( r, p )`][@stdlib/stats/base/dists/negative-binomial/mean]</span><span class="delimiter">: </span><span class="description">negative binomial distribution expected value.</span>
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- <span class="signature">[`mode( r, p )`][@stdlib/stats/base/dists/negative-binomial/mode]</span><span class="delimiter">: </span><span class="description">negative binomial distribution mode.</span>
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- <span class="signature">[`skewness( r, p )`][@stdlib/stats/base/dists/negative-binomial/skewness]</span><span class="delimiter">: </span><span class="description">negative binomial distribution skewness.</span>
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- <span class="signature">[`stdev( r, p )`][@stdlib/stats/base/dists/negative-binomial/stdev]</span><span class="delimiter">: </span><span class="description">negative binomial distribution standard deviation.</span>
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- <span class="signature">[`variance( r, p )`][@stdlib/stats/base/dists/negative-binomial/variance]</span><span class="delimiter">: </span><span class="description">negative binomial 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 [negative binomial][negative-binomial-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">[`NegativeBinomial( [r, p] )`][@stdlib/stats/base/dists/negative-binomial/ctor]</span><span class="delimiter">: </span><span class="description">negative binomial distribution constructor.</span>
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</div>
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<!-- </toc> -->
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```javascript
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var NegativeBinomial = require( '@stdlib/stats/base/dists/negative-binomial' ).NegativeBinomial;
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var dist = new NegativeBinomial( 4.0, 0.2 );
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var y = dist.pmf( 4.0 );
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// returns ~0.023
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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 negativeBinomial = require( '@stdlib/stats/base/dists/negative-binomial' );
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console.log( objectKeys( negativeBinomial ) );
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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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[negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution
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<!-- <toc-links> -->
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[@stdlib/stats/base/dists/negative-binomial/ctor]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/ctor
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[@stdlib/stats/base/dists/negative-binomial/kurtosis]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/kurtosis
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[@stdlib/stats/base/dists/negative-binomial/mean]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/mean
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[@stdlib/stats/base/dists/negative-binomial/mode]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/mode
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[@stdlib/stats/base/dists/negative-binomial/skewness]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/skewness
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[@stdlib/stats/base/dists/negative-binomial/stdev]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/stdev
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[@stdlib/stats/base/dists/negative-binomial/variance]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/variance
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[@stdlib/stats/base/dists/negative-binomial/cdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/cdf
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[@stdlib/stats/base/dists/negative-binomial/logpmf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/logpmf
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[@stdlib/stats/base/dists/negative-binomial/mgf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/mgf
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[@stdlib/stats/base/dists/negative-binomial/pmf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/pmf
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[@stdlib/stats/base/dists/negative-binomial/quantile]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/negative-binomial/quantile
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<!-- </toc-links> -->
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</section>
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<!-- /.links -->
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