npm package: @stdlib/stats-base-dists-t-ctor
Description: Student's t distribution constructor.
Author: The Stdlib Authors
Latest version: 0.2.3

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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 constructor.

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### T( \[v] )

Returns a [Student's t][t-distribution] distribution object.

```javascript
var t = new T();

var mu = t.mean;
// returns NaN
```

By default, `v = 1.0`. To create a distribution having a different degrees of freedom `v`, provide a parameter value.

```javascript
var t = new T( 4.0 );

var mu = t.mean;
// returns 0.0
```

* * *

## t

A [Student's t][t-distribution] distribution object has the following properties and methods...

### Writable Properties

#### t.v

Degrees of freedom of the distribution. `v` **must** be a positive number.

```javascript
var t = new T( 2.0 );

var v = t.v;
// returns 2.0

t.v = 3.0;

v = t.v;
// returns 3.0
```

* * *

### Computed Properties

#### T.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var t = new T( 4.0 );

var entropy = t.entropy;
// returns ~1.682
```

#### T.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var t = new T( 4.0 );

var kurtosis = t.kurtosis;
// returns Infinity
```

#### T.prototype.mean

Returns the [expected value][expected-value].

```javascript
var t = new T( 4.0 );

var mu = t.mean;
// returns 0.0
```

#### T.prototype.median

Returns the [median][median].

```javascript
var t = new T( 4.0 );

var median = t.median;
// returns 0.0
```

#### T.prototype.mode

Returns the [mode][mode].

```javascript
var t = new T( 4.0 );

var mode = t.mode;
// returns 0.0
```

#### T.prototype.skewness

Returns the [skewness][skewness].

```javascript
var t = new T( 4.0 );

var skewness = t.skewness;
// returns 0.0
```

#### T.prototype.stdev

Returns the [standard deviation][standard-deviation].

```javascript
var t = new T( 4.0 );

var s = t.stdev;
// returns ~1.414
```

#### T.prototype.variance

Returns the [variance][variance].

```javascript
var t = new T( 4.0 );

var s2 = t.variance;
// returns 2.0
```

* * *

### Methods

#### T.prototype.cdf( x )

Evaluates the [cumulative distribution function][cdf] (CDF).

```javascript
var t = new T( 2.0 );

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

#### T.prototype.logcdf( x )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).

```javascript
var t = new T( 2.0 );

var y = t.logcdf( 0.5 );
// returns ~-0.405
```

#### T.prototype.logpdf( x )

Evaluates the natural logarithm of the [probability density function][pdf] (PDF).

```javascript
var t = new T( 2.0 );

var y = t.logpdf( 0.8 );
// returns ~-1.456
```

#### T.prototype.pdf( x )

Evaluates the [probability density function][pdf] (PDF).

```javascript
var t = new T( 2.0 );

var y = t.pdf( 0.8 );
// returns ~0.233
```

#### T.prototype.quantile( p )

Evaluates the [quantile function][quantile-function] at probability `p`.

```javascript
var t = new T( 2.0 );

var y = t.quantile( 0.5 );
// returns 0.0

y = t.quantile( 1.9 );
// returns NaN
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

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

var t = new T( 2.0 );

var mu = t.mean;
// returns 0.0

var mode = t.mode;
// returns 0.0

var s2 = t.variance;
// returns Infinity

var y = t.cdf( 0.8 );
// returns ~0.746
```

</section>

<!-- /.examples -->

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</section>

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</section>

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

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].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-t-ctor/main/LICENSE

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

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[expected-value]: https://en.wikipedia.org/wiki/Expected_value

[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis

[median]: https://en.wikipedia.org/wiki/Median

[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29

[skewness]: https://en.wikipedia.org/wiki/Skewness

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

[variance]: https://en.wikipedia.org/wiki/Variance

</section>

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