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

Standard library statistical functions.

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# Binomial

> Binomial distribution.

<section class="usage">

## Usage

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

#### binomial

Binomial distribution.

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

The namespace contains the following distribution functions:

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

<div class="namespace-toc">

-   <span class="signature">[`cdf( x, n, p )`][@stdlib/stats/base/dists/binomial/cdf]</span><span class="delimiter">: </span><span class="description">binomial distribution cumulative distribution function.</span>
-   <span class="signature">[`logpmf( x, n, p )`][@stdlib/stats/base/dists/binomial/logpmf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the probability mass function (PMF) for a binomial distribution.</span>
-   <span class="signature">[`mgf( t, n, p )`][@stdlib/stats/base/dists/binomial/mgf]</span><span class="delimiter">: </span><span class="description">binomial distribution moment-generating function (MGF).</span>
-   <span class="signature">[`pmf( x, n, p )`][@stdlib/stats/base/dists/binomial/pmf]</span><span class="delimiter">: </span><span class="description">binomial distribution probability mass function (PMF).</span>
-   <span class="signature">[`quantile( r, n, p )`][@stdlib/stats/base/dists/binomial/quantile]</span><span class="delimiter">: </span><span class="description">binomial distribution quantile function.</span>

</div>

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The namespace contains the following functions for calculating distribution properties:

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<div class="namespace-toc">

-   <span class="signature">[`entropy( n, p )`][@stdlib/stats/base/dists/binomial/entropy]</span><span class="delimiter">: </span><span class="description">binomial distribution entropy.</span>
-   <span class="signature">[`kurtosis( n, p )`][@stdlib/stats/base/dists/binomial/kurtosis]</span><span class="delimiter">: </span><span class="description">binomial distribution excess kurtosis.</span>
-   <span class="signature">[`mean( n, p )`][@stdlib/stats/base/dists/binomial/mean]</span><span class="delimiter">: </span><span class="description">binomial distribution expected value.</span>
-   <span class="signature">[`median( n, p )`][@stdlib/stats/base/dists/binomial/median]</span><span class="delimiter">: </span><span class="description">binomial distribution median.</span>
-   <span class="signature">[`mode( n, p )`][@stdlib/stats/base/dists/binomial/mode]</span><span class="delimiter">: </span><span class="description">binomial distribution mode.</span>
-   <span class="signature">[`skewness( n, p )`][@stdlib/stats/base/dists/binomial/skewness]</span><span class="delimiter">: </span><span class="description">binomial distribution skewness.</span>
-   <span class="signature">[`stdev( n, p )`][@stdlib/stats/base/dists/binomial/stdev]</span><span class="delimiter">: </span><span class="description">binomial distribution standard deviation.</span>
-   <span class="signature">[`variance( n, p )`][@stdlib/stats/base/dists/binomial/variance]</span><span class="delimiter">: </span><span class="description">binomial distribution variance.</span>

</div>

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

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<div class="namespace-toc">

-   <span class="signature">[`Binomial( [n, p] )`][@stdlib/stats/base/dists/binomial/ctor]</span><span class="delimiter">: </span><span class="description">binomial distribution constructor.</span>

</div>

<!-- </toc> -->

```javascript
var Binomial = require( '@stdlib/stats/base/dists/binomial' ).Binomial;
var dist = new Binomial( 10, 0.4 );

var mu = dist.mean;
// returns 4
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- TODO: better examples -->

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

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

/*
* Let's take an example of rolling a fair dice 10 times and counting the number of times a 6 is rolled.
* This situation can be modeled using a Binomial distribution with n = 10 and p = 1/6
*/

var n = 10;
var p = 1/6;

// Mean can be used to calculate the average number of times a 6 is rolled:
console.log( binomial.mean( n, p ) );
// => ~1.6667

// PMF can be used to calculate the probability of getting a certain number of 6s (say 3 sixes):
console.log( binomial.pmf( 3, n, p ) );
// => ~0.1550

// CDF can be used to calculate probability up to certain number of 6s (say up to 3 sixes):
console.log( binomial.cdf( 3, n, p ) );
// => ~0.9303

// Quantile can be used to calculate the number of 6s at which you can be 80% confident that the actual number will not exceed.
console.log( binomial.quantile( 0.8, n, p ) );
// => 3

// Standard deviation can be used to calculate the measure of the spread of 6s around the mean:
console.log( binomial.stdev( n, p ) );
// => ~1.1785

// Skewness can be used to calculate the asymmetry of the distribution of 6s:
console.log( binomial.skewness( n, p ) );
// => ~0.5657

// MGF can be used for more advanced statistical analyses and generating moments of the distribution:
console.log( binomial.mgf( 0.5, n, p ) );
// => ~2.7917
```

</section>

<!-- /.examples -->

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<section class="related">

</section>

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<section class="links">

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

<!-- <toc-links> -->

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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</section>

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