@stdlib/stats-base-dists-frechet-pdf
v0.2.3TypeScript
Fréchet distribution probability density function (PDF).
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Published by The Stdlib Authors
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Probability Density Function
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> [Fréchet][frechet-distribution] distribution [probability density function][pdf].
The [probability density function][pdf] for a [Fréchet][frechet-distribution] random variable is
where alpha > 0 is the shape, s > 0 the scale and m the location parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-frechet-pdf
Usage
`javascript`
var pdf = require( '@stdlib/stats-base-dists-frechet-pdf' );
#### pdf( x, alpha, s, m )
Evaluates the [probability density function][pdf] (PDF) for a [Fréchet][frechet-distribution] distribution with shape alpha, scale s, and location m at a value x.
`javascript
var y = pdf( 10.0, 2.0, 3.0, 5.0 );
// returns ~0.1
y = pdf( -3.0, 1.0, 2.0, -4.0 );
// returns ~0.271
y = pdf( 0.0, 2.0, 1.0, -1.0 );
// returns ~0.736
`
If provided x <= m, the function returns 0.
`javascript`
y = pdf( -2.0, 2.0, 1.0, -1.0 );
// returns 0.0
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pdf( NaN, 1.0, 1.0, 0.0 );
// returns NaN
y = pdf( 0.0, NaN, 1.0, 0.0 );
// returns NaN
y = pdf( 0.0, 1.0, NaN, 0.0);
// returns NaN
y = pdf( 0.0, 1.0, 1.0, NaN );
// returns NaN
`
If provided alpha <= 0, the function returns NaN.
`javascript
var y = pdf( 2.0, -0.1, 1.0, 1.0 );
// returns NaN
y = pdf( 2.0, 0.0, 1.0, 1.0 );
// returns NaN
`
If provided s <= 0, the function returns NaN.
`javascript
var y = pdf( 2.0, 1.0, -1.0, 1.0 );
// returns NaN
y = pdf( 2.0, 1.0, 0.0, 1.0 );
// returns NaN
`
#### pdf.factory( alpha, s, m )
Returns a function for evaluating the [probability density function][pdf] of a [Fréchet][frechet-distribution] distribution with shape alpha, scale s, and location m.
`javascript
var mypdf = pdf.factory( 3.0, 3.0, 5.0 );
var y = mypdf( 10.0 );
// returns ~0.104
y = mypdf( 7.0 );
// returns ~0.173
`
Examples
`javascript
var randu = require( '@stdlib/random-base-randu' );
var pdf = require( '@stdlib/stats-base-dists-frechet-pdf' );
var alpha;
var m;
var s;
var x;
var y;
var i;
for ( i = 0; i < 100; i++ ) {
alpha = randu() * 10.0;
x = randu() * 10.0;
s = randu() * 10.0;
m = randu() * 10.0;
y = pdf( x, alpha, s, m );
console.log( 'x: %d, α: %d, s: %d, m: %d, f(x;α,s,m): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}
`
*
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 © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-frechet-pdf
[test-image]: https://github.com/stdlib-js/stats-base-dists-frechet-pdf/actions/workflows/test.yml/badge.svg?branch=v0.2.3
[test-url]: https://github.com/stdlib-js/stats-base-dists-frechet-pdf/actions/workflows/test.yml?query=branch:v0.2.3
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-frechet-pdf/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-frechet-pdf?branch=main
[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg
[chat-url]: https://stdlib.zulipchat.com
[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-pdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-frechet-pdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-frechet-pdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-frechet-pdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-frechet-pdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-frechet-pdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-frechet-pdf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-frechet-pdf/main/LICENSE
[frechet-distribution]: https://en.wikipedia.org/wiki/Fr%C3%A9chet_distribution
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function