@stdlib/stats/base/dists/negative-binomial/README.md

Standard library statistical functions.

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# Negative Binomial

> Negative binomial distribution.

<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:

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<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>

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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>

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

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<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 class="related">

</section>

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<section class="links">

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

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[@stdlib/stats/base/dists/negative-binomial/ctor]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/ctor

[@stdlib/stats/base/dists/negative-binomial/kurtosis]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/kurtosis

[@stdlib/stats/base/dists/negative-binomial/mean]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/mean

[@stdlib/stats/base/dists/negative-binomial/mode]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/mode

[@stdlib/stats/base/dists/negative-binomial/skewness]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/skewness

[@stdlib/stats/base/dists/negative-binomial/stdev]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/stdev

[@stdlib/stats/base/dists/negative-binomial/variance]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/variance

[@stdlib/stats/base/dists/negative-binomial/cdf]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/cdf

[@stdlib/stats/base/dists/negative-binomial/logpmf]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/logpmf

[@stdlib/stats/base/dists/negative-binomial/mgf]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/mgf

[@stdlib/stats/base/dists/negative-binomial/pmf]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/pmf

[@stdlib/stats/base/dists/negative-binomial/quantile]: https://github.com/stdlib-js/stats/tree/main/base/dists/negative-binomial/quantile

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</section>

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