npm package: @stdlib/stats-base-dists-t
Description: Student's t distribution.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Student's T

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Student's t distribution.

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-t
```

</section>

<section class="usage">

## Usage

```javascript
var t = require( '@stdlib/stats-base-dists-t' );
```

#### t

Student's t distribution.

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

The namespace contains the following distribution functions:

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

<div class="namespace-toc">

-   <span class="signature">[`cdf( x, v )`][@stdlib/stats/base/dists/t/cdf]</span><span class="delimiter">: </span><span class="description">Student's t distribution cumulative distribution function (CDF).</span>
-   <span class="signature">[`logcdf( x, v )`][@stdlib/stats/base/dists/t/logcdf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the cumulative distribution function (CDF) for a Student's t distribution.</span>
-   <span class="signature">[`logpdf( x, v )`][@stdlib/stats/base/dists/t/logpdf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the probability density function (PDF) for a Student's t distribution.</span>
-   <span class="signature">[`pdf( x, v )`][@stdlib/stats/base/dists/t/pdf]</span><span class="delimiter">: </span><span class="description">Student's t distribution probability density function (PDF).</span>
-   <span class="signature">[`quantile( p, v )`][@stdlib/stats/base/dists/t/quantile]</span><span class="delimiter">: </span><span class="description">Student's t 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">[`entropy( v )`][@stdlib/stats/base/dists/t/entropy]</span><span class="delimiter">: </span><span class="description">Student's t distribution differential entropy.</span>
-   <span class="signature">[`kurtosis( v )`][@stdlib/stats/base/dists/t/kurtosis]</span><span class="delimiter">: </span><span class="description">Student's t distribution excess kurtosis.</span>
-   <span class="signature">[`mean( v )`][@stdlib/stats/base/dists/t/mean]</span><span class="delimiter">: </span><span class="description">Student's t distribution expected value.</span>
-   <span class="signature">[`median( v )`][@stdlib/stats/base/dists/t/median]</span><span class="delimiter">: </span><span class="description">Student's t distribution median.</span>
-   <span class="signature">[`mode( v )`][@stdlib/stats/base/dists/t/mode]</span><span class="delimiter">: </span><span class="description">Student's t distribution mode.</span>
-   <span class="signature">[`skewness( v )`][@stdlib/stats/base/dists/t/skewness]</span><span class="delimiter">: </span><span class="description">Student's t distribution skewness.</span>
-   <span class="signature">[`stdev( v )`][@stdlib/stats/base/dists/t/stdev]</span><span class="delimiter">: </span><span class="description">Student's t distribution standard deviation.</span>
-   <span class="signature">[`variance( v )`][@stdlib/stats/base/dists/t/variance]</span><span class="delimiter">: </span><span class="description">Student's t distribution variance.</span>

</div>

<!-- </toc> -->

The namespace contains a constructor function for creating a [Student's t][t-distribution] distribution object.

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

<div class="namespace-toc">

-   <span class="signature">[`T( [v] )`][@stdlib/stats/base/dists/t/ctor]</span><span class="delimiter">: </span><span class="description">Student's t distribution constructor.</span>

</div>

<!-- </toc> -->

```javascript
var T = require( '@stdlib/stats-base-dists-t' ).T;

var dist = new T( 2.0 );

var y = dist.cdf( 0.5 );
// returns ~0.667
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- TODO: better examples -->

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

```javascript
var t = require( '@stdlib/stats-base-dists-t' );

var dof = 3;
var x = 1.5;

// Evaluate the probability density function (PDF) at a specific value:
var res = t.pdf( x, dof );
console.log( 'PDF at x = ' + x + ': ' + res );

// Evaluate the cumulative distribution function (CDF) at a specific value:
res = t.cdf( x, dof );
console.log( 'CDF at x = ' + x + ': ' + res );

// Get the mean and variance of the t distribution:
var mu = t.mean( dof );
var v = t.variance( dof );
console.log( 'Mean: ' + mu + ', Variance: ' + v );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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[t-distribution]: https://en.wikipedia.org/wiki/Student%27s_t-distribution

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

[@stdlib/stats/base/dists/t/ctor]: https://www.npmjs.com/package/@stdlib/stats-base-dists-t-ctor

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[@stdlib/stats/base/dists/t/mean]: https://www.npmjs.com/package/@stdlib/stats-base-dists-t-mean

[@stdlib/stats/base/dists/t/median]: https://www.npmjs.com/package/@stdlib/stats-base-dists-t-median

[@stdlib/stats/base/dists/t/mode]: https://www.npmjs.com/package/@stdlib/stats-base-dists-t-mode

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