https://github.com/stdlib-js/stats-base-dists-frechet-mean
Fréchet distribution expected value.
https://github.com/stdlib-js/stats-base-dists-frechet-mean
average avg center continuous dist distribution expectation extreme frechet inverse javascript location mean node node-js nodejs statistics stats stdlib weibull
Last synced: 3 months ago
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Fréchet distribution expected value.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-base-dists-frechet-mean
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:29:56.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2025-06-29T02:47:39.000Z (3 months ago)
- Last Synced: 2025-06-29T03:39:48.669Z (3 months ago)
- Topics: average, avg, center, continuous, dist, distribution, expectation, extreme, frechet, inverse, javascript, location, mean, node, node-js, nodejs, statistics, stats, stdlib, weibull
- Language: Python
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 1.03 MB
- Stars: 2
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
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README
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# Mean
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> [Fréchet][frechet-distribution] distribution [expected value][mean].
The [expected value][mean] for a [Fréchet][frechet-distribution] random variable shape `α > 0`, scale `s > 0`, and location parameter `m` is
```math
\mathbb{E}\left[ X \right] = \begin{cases}\ m+s\Gamma\left(1-{\frac{1}{\alpha}}\right) & {\text{ for }}\alpha >1\\\ \infty & {\text{ otherwise }}\end{cases}
```
where `Γ` is the [gamma function][gamma-function].
## Installation
```bash
npm install @stdlib/stats-base-dists-frechet-mean
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var mean = require( '@stdlib/stats-base-dists-frechet-mean' );
```
#### mean( alpha, s, m )
Returns the [expected value][mean] for a [Fréchet][frechet-distribution] distribution with shape `alpha > 0`, scale `s > 0`, and location parameter `m`.
```javascript
var y = mean( 2.0, 1.0, 1.0 );
// returns ~2.772
y = mean( 4.0, 4.0, -1.0 );
// returns ~3.902
y = mean( 1.0, 1.0, 2.0 );
// returns Infinity
```
If provided `NaN` as any argument, the function returns `NaN`.
```javascript
var y = mean( NaN, 1.0, -2.0 );
// returns NaN
y = mean( 1.0, NaN, -2.0 );
// returns NaN
y = mean( 1.0, 1.0, NaN );
// returns NaN
```
If provided `alpha <= 0`, the function returns `NaN`.
```javascript
var y = mean( 0.0, 3.0, 2.0 );
// returns NaN
y = mean( 0.0, -1.0, 2.0 );
// returns NaN
```
If provided `s <= 0`, the function returns `NaN`.
```javascript
var y = mean( 1.0, 0.0, 2.0 );
// returns NaN
y = mean( 1.0, -1.0, 2.0 );
// returns NaN
```
## Examples
```javascript
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var mean = require( '@stdlib/stats-base-dists-frechet-mean' );
var alpha;
var m;
var s;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
alpha = ( randu()*20.0 ) + EPS;
s = ( randu()*20.0 ) + EPS;
m = ( randu()*40.0 ) - 20.0;
y = mean( alpha, s, m );
console.log( 'α: %d, s: %d, m: %d, E(X;α,s,m): %d', alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}
```
* * *
## C APIs
### Usage
```c
#include "stdlib/stats/base/dists/frechet/mean.h"
```
#### stdlib_base_dists_frechet_mean( alpha, s, m )
Evaluates the [expected value][mean] for a [Fréchet][frechet-distribution] distribution with shape `alpha > 0`, scale `s > 0`, and location parameter `m`.
```c
double out = stdlib_base_dists_frechet_mean( 5.0, 2.0, 0.0 );
// returns ~2.328
```
The function accepts the following arguments:
- **alpha**: `[in] double` shape parameter.
- **s**: `[in] double` scale parameter.
- **m**: `[in] double` location parameter.
```c
double stdlib_base_dists_frechet_mean( const double alpha, const double s, const double m );
```
### Examples
```c
#include "stdlib/stats/base/dists/frechet/mean.h"
#include "stdlib/constants/float64/eps.h"
#include
#include
static double random_uniform( const double min, const double max ) {
double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
return min + ( v*(max-min) );
}
int main( void ) {
double alpha;
double s;
double m;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
s = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
m = random_uniform( -20.0, 20.0 );
y = stdlib_base_dists_frechet_mean( alpha, s, m );
printf( "α: %lf, s: %lf, m: %lf, E(X;α,s,m): %lf\n", alpha, s, m, y );
}
}
```
* * *
## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-frechet-mean.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-frechet-mean
[test-image]: https://github.com/stdlib-js/stats-base-dists-frechet-mean/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-base-dists-frechet-mean/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-frechet-mean/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-frechet-mean?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-frechet-mean/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-frechet-mean/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-frechet-mean/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-frechet-mean/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-frechet-mean/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-frechet-mean/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-frechet-mean/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-frechet-mean/main/LICENSE
[frechet-distribution]: https://en.wikipedia.org/wiki/Fr%C3%A9chet_distribution
[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
[mean]: https://en.wikipedia.org/wiki/Expected_value