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Gumbel

Gumbel distribution constructor.

Installation

npm install @stdlib/stats-base-dists-gumbel-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 Gumbel = require( '@stdlib/stats-base-dists-gumbel-ctor' );

Gumbel( [mu, beta] )

Returns a Gumbel distribution object.

var gumbel = new Gumbel();

var mean = gumbel.mean;
// returns ~0.577

By default, mu = 0.0 and beta = 1.0. To create a distribution having a different mu (location parameter) and beta (scale parameter), provide the corresponding arguments.

var gumbel = new Gumbel( 2.0, 4.0 );

var mean = gumbel.mean;
// returns ~4.309

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gumbel

A Gumbel distribution object has the following properties and methods...

Writable Properties

gumbel.mu

Location parameter of the distribution.

var gumbel = new Gumbel();

var mu = gumbel.mu;
// returns 0.0

gumbel.mu = 3.0;

mu = gumbel.mu;
// returns 3.0

gumbel.beta

Scale parameter of the distribution. beta must be a positive number.

var gumbel = new Gumbel( 2.0, 4.0 );

var beta = gumbel.beta;
// returns 4.0

gumbel.beta = 3.0;

beta = gumbel.beta;
// returns 3.0

---

Computed Properties

Gumbel.prototype.entropy

Returns the differential entropy.

var gumbel = new Gumbel( 4.0, 12.0 );

var entropy = gumbel.entropy;
// returns ~4.062

Gumbel.prototype.kurtosis

Returns the excess kurtosis.

var gumbel = new Gumbel( 4.0, 12.0 );

var kurtosis = gumbel.kurtosis;
// returns 2.4

Gumbel.prototype.mean

Returns the expected value.

var gumbel = new Gumbel( 4.0, 12.0 );

var mu = gumbel.mean;
// returns ~10.927

Gumbel.prototype.median

Returns the median.

var gumbel = new Gumbel( 4.0, 12.0 );

var median = gumbel.median;
// returns ~8.398

Gumbel.prototype.mode

Returns the mode.

var gumbel = new Gumbel( 4.0, 12.0 );

var mode = gumbel.mode;
// returns 4.0

Gumbel.prototype.skewness

Returns the skewness.

var gumbel = new Gumbel( 4.0, 12.0 );

var skewness = gumbel.skewness;
// returns ~1.14

Gumbel.prototype.stdev

Returns the standard deviation.

var gumbel = new Gumbel( 4.0, 12.0 );

var s = gumbel.stdev;
// returns ~15.391

Gumbel.prototype.variance

Returns the variance.

var gumbel = new Gumbel( 4.0, 12.0 );

var s2 = gumbel.variance;
// returns ~236.871

---

Methods

Gumbel.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.cdf( 0.5 );
// returns ~0.233

Gumbel.prototype.logcdf( x )

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

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.logcdf( 2.0 );
// returns -1.0

Gumbel.prototype.logpdf( x )

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

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.logpdf( 0.8 );
// returns ~-2.436

Gumbel.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.mgf( 0.1 );
// returns ~1.819

Gumbel.prototype.pdf( x )

Evaluates the probability density function (PDF).

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.pdf( 2.0 );
// returns ~0.092

Gumbel.prototype.quantile( p )

Evaluates the quantile function at probability p.

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.quantile( 0.5 );
// returns ~3.466

y = gumbel.quantile( 1.9 );
// returns NaN

---

Examples

var Gumbel = require( '@stdlib/stats-base-dists-gumbel-ctor' );

var gumbel = new Gumbel( 2.0, 4.0 );

var mean = gumbel.mean;
// returns ~4.309

var median = gumbel.median;
// returns ~3.466

var s2 = gumbel.variance;
// returns ~26.319

var y = gumbel.cdf( 0.8 );
// returns ~0.259

---

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 © 2016-2024. The Stdlib Authors.