npm package: @stdlib/stats-base-dists-weibull-ctor
Description: Weibull distribution constructor.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Weibull

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

> Weibull distribution constructor.

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<section class="intro">

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

```javascript
var Weibull = require( '@stdlib/stats-base-dists-weibull-ctor' );
```

#### Weibull( \[k, lambda] )

Returns a [Weibull][weibull-distribution] distribution object.

```javascript
var weibull = new Weibull();

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

By default, `k = 1.0` and `lambda = 1.0`. To create a distribution having a different `k` (shape parameter) and `lambda` (scale parameter), provide the corresponding arguments.

```javascript
var weibull = new Weibull( 2.0, 4.0 );

var mode = weibull.mode;
// returns ~2.828
```

* * *

## weibull

A [Weibull][weibull-distribution] distribution object has the following properties and methods...

### Writable Properties

#### weibull.k

Shape parameter of the distribution. `k` **must** be a positive number.

```javascript
var weibull = new Weibull();

var k = weibull.k;
// returns 1.0

weibull.k = 3.0;

k = weibull.k;
// returns 3.0
```

#### weibull.lambda

Scale parameter of the distribution. `lambda` **must** be a positive number.

```javascript
var weibull = new Weibull( 2.0, 4.0 );

var lambda = weibull.lambda;
// returns 4.0

weibull.lambda = 3.0;

lambda = weibull.lambda;
// returns 3.0
```

* * *

### Computed Properties

#### Weibull.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var weibull = new Weibull( 4.0, 12.0 );

var entropy = weibull.entropy;
// returns ~2.532
```

#### Weibull.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var weibull = new Weibull( 4.0, 12.0 );

var kurtosis = weibull.kurtosis;
// returns ~-0.252
```

#### Weibull.prototype.mean

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

```javascript
var weibull = new Weibull( 4.0, 12.0 );

var mu = weibull.mean;
// returns ~10.877
```

#### Weibull.prototype.mode

Returns the [mode][mode].

```javascript
var weibull = new Weibull( 4.0, 12.0 );

var mode = weibull.mode;
// returns ~11.167
```

#### Weibull.prototype.skewness

Returns the [skewness][skewness].

```javascript
var weibull = new Weibull( 4.0, 12.0 );

var skewness = weibull.skewness;
// returns ~-0.087
```

#### Weibull.prototype.stdev

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

```javascript
var weibull = new Weibull( 4.0, 12.0 );

var s = weibull.stdev;
// returns ~3.051
```

#### Weibull.prototype.variance

Returns the [variance][variance].

```javascript
var weibull = new Weibull( 4.0, 12.0 );

var s2 = weibull.variance;
// returns ~9.311
```

* * *

### Methods

#### Weibull.prototype.cdf( x )

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

```javascript
var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.cdf( 0.5 );
// returns ~0.016
```

#### Weibull.prototype.logcdf( x )

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

```javascript
var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.logcdf( 0.8 );
// returns ~-3.239
```

#### Weibull.prototype.logpdf( x )

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

```javascript
var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.logpdf( 0.8 );
// returns ~-2.343
```

#### Weibull.prototype.mgf( t )

Evaluates the [moment-generating function][mgf] (MGF).

```javascript
var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.mgf( 0.5 );
// returns ~9.878
```

#### Weibull.prototype.pdf( x )

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

```javascript
var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.pdf( 0.8 );
// returns ~0.096
```

#### Weibull.prototype.quantile( p )

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

```javascript
var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.quantile( 0.5 );
// returns ~3.33

y = weibull.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 Weibull = require( '@stdlib/stats-base-dists-weibull-ctor' );

var weibull = new Weibull( 2.0, 4.0 );

var mu = weibull.mean;
// returns ~3.545

var mode = weibull.mode;
// returns ~2.828

var s2 = weibull.variance;
// returns ~3.434

var y = weibull.cdf( 0.8 );
// returns ~0.039
```

</section>

<!-- /.examples -->

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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-weibull-ctor/main/LICENSE

[weibull-distribution]: https://en.wikipedia.org/wiki/Weibull_distribution

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

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_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

[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

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