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Weibull

Weibull distribution constructor.

Installation

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

Weibull( [k, lambda] )

Returns a Weibull distribution object.

var weibull = new Weibull();

var mode = weibull.mode;
// returns 0.0

By default, k = 1.0 and lambda = 1.0. To create a distribution having a different k (shape parameter) and lambda (scale parameter), provide the corresponding arguments.

var weibull = new Weibull( 2.0, 4.0 );

var mode = weibull.mode;
// returns ~2.828

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weibull

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

Writable Properties

weibull.k

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

var weibull = new Weibull();

var k = weibull.k;
// returns 1.0

weibull.k = 3.0;

k = weibull.k;
// returns 3.0

weibull.lambda

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

var weibull = new Weibull( 2.0, 4.0 );

var lambda = weibull.lambda;
// returns 4.0

weibull.lambda = 3.0;

lambda = weibull.lambda;
// returns 3.0

---

Computed Properties

Weibull.prototype.entropy

Returns the differential entropy.

var weibull = new Weibull( 4.0, 12.0 );

var entropy = weibull.entropy;
// returns ~2.532

Weibull.prototype.kurtosis

Returns the excess kurtosis.

var weibull = new Weibull( 4.0, 12.0 );

var kurtosis = weibull.kurtosis;
// returns ~-0.252

Weibull.prototype.mean

Returns the expected value.

var weibull = new Weibull( 4.0, 12.0 );

var mu = weibull.mean;
// returns ~10.877

Weibull.prototype.mode

Returns the mode.

var weibull = new Weibull( 4.0, 12.0 );

var mode = weibull.mode;
// returns ~11.167

Weibull.prototype.skewness

Returns the skewness.

var weibull = new Weibull( 4.0, 12.0 );

var skewness = weibull.skewness;
// returns ~-0.087

Weibull.prototype.stdev

Returns the standard deviation.

var weibull = new Weibull( 4.0, 12.0 );

var s = weibull.stdev;
// returns ~3.051

Weibull.prototype.variance

Returns the variance.

var weibull = new Weibull( 4.0, 12.0 );

var s2 = weibull.variance;
// returns ~9.311

---

Methods

Weibull.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.cdf( 0.5 );
// returns ~0.016

Weibull.prototype.logcdf( x )

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

var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.logcdf( 0.8 );
// returns ~-3.239

Weibull.prototype.logpdf( x )

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

var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.logpdf( 0.8 );
// returns ~-2.343

Weibull.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.mgf( 0.5 );
// returns ~9.878

Weibull.prototype.pdf( x )

Evaluates the probability density function (PDF).

var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.pdf( 0.8 );
// returns ~0.096

Weibull.prototype.quantile( p )

Evaluates the quantile function at probability p.

var weibull = new Weibull( 2.0, 4.0 );

var y = weibull.quantile( 0.5 );
// returns ~3.33

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

---

Examples

var Weibull = require( '@stdlib/stats-base-dists-weibull-ctor' );

var weibull = new Weibull( 2.0, 4.0 );

var mu = weibull.mean;
// returns ~3.545

var mode = weibull.mode;
// returns ~2.828

var s2 = weibull.variance;
// returns ~3.434

var y = weibull.cdf( 0.8 );
// returns ~0.039

---

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.