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

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# Fréchet

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

> Fréchet 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>

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<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### Frechet( \[alpha, s, m] )

Returns a [Fréchet][frechet-distribution] distribution object.

```javascript
var frechet = new Frechet();

var mu = frechet.mean;
// returns Infinity
```

By default, `alpha = 1.0`, `s = 1.0`, and `m = 0.0`. To create a distribution having a different `alpha` (shape), `s` (scale), and `m` (location), provide the corresponding arguments.

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.5 );

var mu = frechet.mean;
// returns ~10.59
```

* * *

## frechet

An [Fréchet][frechet-distribution] distribution object has the following properties and methods...

### Writable Properties

#### frechet.alpha

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

```javascript
var frechet = new Frechet();

var alpha = frechet.alpha;
// returns 1.0

frechet.alpha = 0.5;

alpha = frechet.alpha;
// returns 0.5
```

#### frechet.s

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 1.5 );

var s = frechet.s;
// returns 4.0

frechet.s = 3.0;

s = frechet.s;
// returns 3.0
```

#### frechet.m

Location parameter of the distribution.

```javascript
var frechet = new Frechet( 2.0, 2.0, 4.0 );

var m = frechet.m;
// returns 4.0

frechet.m = 3.0;

m = frechet.m;
// returns 3.0
```

* * *

### Computed Properties

#### Frechet.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var entropy = frechet.entropy;
// returns ~2.82
```

#### Frechet.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

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

#### Frechet.prototype.mean

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

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var mu = frechet.mean;
// returns ~16.705
```

#### Frechet.prototype.median

Returns the [median][median].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var median = frechet.median;
// returns ~15.151
```

#### Frechet.prototype.mode

Returns the [mode][mode].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var mode = frechet.mode;
// returns ~13.349
```

#### Frechet.prototype.skewness

Returns the [skewness][skewness].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var skewness = frechet.skewness;
// returns ~5.605
```

#### Frechet.prototype.stdev

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

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var s = frechet.stdev;
// returns ~6.245
```

#### Frechet.prototype.variance

Returns the [variance][variance].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var s2 = frechet.variance;
// returns ~38.996
```

* * *

### Methods

#### Frechet.prototype.cdf( x )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.cdf( 2.5 );
// returns 0.0
```

#### Frechet.prototype.logcdf( x )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.logcdf( 2.5 );
// returns -Infinity
```

#### Frechet.prototype.logpdf( x )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.logpdf( 5.5 );
// returns ~-1.843
```

#### Frechet.prototype.pdf( x )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.pdf( 5.5 );
// returns ~0.158
```

#### Frechet.prototype.quantile( p )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.quantile( 0.5 );
// returns ~7.804

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

</section>

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<section class="notes">

</section>

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<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

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

var frechet = new Frechet( 2.0, 4.0, 3.0 );

var mu = frechet.mean;
// returns ~10.09

var median = frechet.median;
// returns ~7.804

var s2 = frechet.variance;
// returns Infinity

var y = frechet.cdf( 2.5 );
// returns 0.0
```

</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].

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

[frechet-distribution]: https://en.wikipedia.org/wiki/Fr%C3%A9chet_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

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[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

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