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Beta

Beta distribution constructor.

Installation

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

Beta( [alpha, beta] )

Returns a beta distribution object.

var beta = new Beta();

var mu = beta.mean;
// returns 0.5

By default, alpha = 1.0 and beta = 1.0. To create a distribution having a different alpha (first shape parameter) and beta (second shape parameter), provide the corresponding arguments.

var beta = new Beta( 2.0, 4.0 );

var mu = beta.mean;
// returns ~0.333

---

beta

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

Writable Properties

beta.alpha

First shape parameter of the distribution. alpha must be a positive number.

var beta = new Beta();

var alpha = beta.alpha;
// returns 1.0

beta.alpha = 3.0;

alpha = beta.alpha;
// returns 3.0

beta.beta

Second shape parameter of the distribution. beta must be a positive number.

var beta = new Beta( 2.0, 4.0 );

var b = beta.beta;
// returns 4.0

beta.beta = 3.0;

b = beta.beta;
// returns 3.0

---

Computed Properties

Beta.prototype.entropy

Returns the differential entropy.

var beta = new Beta( 4.0, 12.0 );

var entropy = beta.entropy;
// returns ~-0.869

Beta.prototype.kurtosis

Returns the excess kurtosis.

var beta = new Beta( 4.0, 12.0 );

var kurtosis = beta.kurtosis;
// returns ~0.082

Beta.prototype.mean

Returns the expected value.

var beta = new Beta( 4.0, 12.0 );

var mu = beta.mean;
// returns 0.25

Beta.prototype.median

Returns the median.

var beta = new Beta( 4.0, 12.0 );

var median = beta.median;
// returns ~0.239

Beta.prototype.mode

Returns the mode.

var beta = new Beta( 4.0, 12.0 );

var mode = beta.mode;
// returns ~0.214

Beta.prototype.skewness

Returns the skewness.

var beta = new Beta( 4.0, 12.0 );

var skewness = beta.skewness;
// returns ~0.529

Beta.prototype.stdev

Returns the standard deviation.

var beta = new Beta( 4.0, 12.0 );

var s = beta.stdev;
// returns ~0.105

Beta.prototype.variance

Returns the variance.

var beta = new Beta( 4.0, 12.0 );

var s2 = beta.variance;
// returns ~0.011

---

Methods

Beta.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var beta = new Beta( 2.0, 4.0 );

var y = beta.cdf( 0.5 );
// returns ~0.813

Beta.prototype.logcdf( x )

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

var beta = new Beta( 2.0, 4.0 );

var y = beta.logcdf( 0.5 );
// returns ~-0.208

Beta.prototype.logpdf( x )

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

var beta = new Beta( 2.0, 4.0 );

var y = beta.logpdf( 0.8 );
// returns ~-2.0557

Beta.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var beta = new Beta( 2.0, 4.0 );

var y = beta.mgf( 0.5 );
// returns ~1.186

Beta.prototype.pdf( x )

Evaluates the probability density function (PDF).

var beta = new Beta( 2.0, 4.0 );

var y = beta.pdf( 0.8 );
// returns ~0.128

Beta.prototype.quantile( p )

Evaluates the quantile function at probability p.

var beta = new Beta( 2.0, 4.0 );

var y = beta.quantile( 0.5 );
// returns ~0.314

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

---

Examples

var Beta = require( '@stdlib/stats-base-dists-beta-ctor' );

var beta = new Beta( 2.0, 4.0 );

var mu = beta.mean;
// returns ~0.333

var median = beta.median;
// returns ~0.314

var s2 = beta.variance;
// returns ~0.032

var y = beta.cdf( 0.8 );
// returns ~0.993

---

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.