npm package: @stdlib/stats-base-dists-negative-binomial
Description: Negative binomial distribution.
Author: The Stdlib Authors
Latest version: 0.2.2

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# Negative Binomial

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> Negative binomial distribution.

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-negative-binomial
```

</section>

<section class="usage">

## Usage

```javascript
var negativeBinomial = require( '@stdlib/stats-base-dists-negative-binomial' );
```

#### negativeBinomial

Negative binomial distribution.

```javascript
var dist = negativeBinomial;
// returns {...}
```

The namespace contains the following distribution functions:

<!-- <toc pattern="*+(cdf|pmf|mgf|quantile)*"> -->

<div class="namespace-toc">

-   <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>
-   <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>
-   <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>
-   <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>
-   <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>

</div>

<!-- </toc> -->

The namespace contains the following functions for calculating distribution properties:

<!-- <toc pattern="*+(entropy|kurtosis|mean|median|mode|skewness|stdev|variance)*"> -->

<div class="namespace-toc">

-   <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>
-   <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>
-   <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>
-   <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>
-   <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>
-   <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>

</div>

<!-- </toc> -->

The namespace contains a constructor function for creating a [negative binomial][negative-binomial-distribution] distribution object.

<!-- <toc pattern="*ctor*"> -->

<div class="namespace-toc">

-   <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>

</div>

<!-- </toc> -->

```javascript
var NegativeBinomial = require( '@stdlib/stats-base-dists-negative-binomial' ).NegativeBinomial;

var dist = new NegativeBinomial( 4.0, 0.2 );

var y = dist.pmf( 4.0 );
// returns ~0.023
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- TODO: better examples -->

<!-- eslint no-undef: "error" -->

```javascript
var negativeBinomial = require( '@stdlib/stats-base-dists-negative-binomial' );

/*
* Let's take an example of flipping a biased coin until getting 5 heads.
* This situation can be modeled using a Negative Binomial distribution with r = 5 and p = 1/2.
*/

var r = 5.0;
var p = 1/2;

// Mean can be used to calculate the average number of trials needed to get 5 heads:
console.log( negativeBinomial.mean( r, p ) );
// => 5

// PMF can be used to calculate the probability of getting heads on a specific trial (say on the 8th trial):
console.log( negativeBinomial.pmf( 8, r, p ) );
// => ~0.06

// CDF can be used to calculate the probability up to a certain number of trials (say up to 8 trials):
console.log( negativeBinomial.cdf( 8, r, p ) );
// => ~0.867

// Quantile can be used to calculate the number of trials at which you can be 80% confident that the actual number will not exceed:
console.log( negativeBinomial.quantile( 0.8, r, p ) );
// => 7

// Standard deviation can be used to calculate the measure of the spread of trials around the mean:
console.log( negativeBinomial.stdev( r, p ) );
// => ~3.162

// Skewness can be used to calculate the asymmetry of the distribution of trials:
console.log( negativeBinomial.skewness( r, p ) );
// => ~0.949

// MGF can be used for more advanced statistical analyses and generating moments of the distribution:
console.log( negativeBinomial.mgf( 0.5, r, p ) );
// => ~2277.597
```

</section>

<!-- /.examples -->

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</section>

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For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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[negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution

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