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Fréchet

Fréchet distribution constructor.

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

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

Frechet( [alpha, s, m] )

Returns a Fréchet distribution object.

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.

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

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

---

frechet

An Fréchet distribution object has the following properties and methods...

Writable Properties

frechet.alpha

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

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.

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.

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.

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

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

Frechet.prototype.kurtosis

Returns the excess kurtosis.

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

var kurtosis = frechet.kurtosis;
// returns Infinity

Frechet.prototype.mean

Returns the expected value.

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

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

Frechet.prototype.median

Returns the median.

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

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

Frechet.prototype.mode

Returns the mode.

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

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

Frechet.prototype.skewness

Returns the skewness.

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

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

Frechet.prototype.stdev

Returns the standard deviation.

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

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

Frechet.prototype.variance

Returns the variance.

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).

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).

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).

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).

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 at probability p.

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

---

Examples

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

---

Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.