Beta

Beta distribution constructor.

Usage

var Beta = require( '@stdlib/math/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 parameter values.

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 0.25

Beta.prototype.skewness

Returns the skewness.

var beta = new Beta( 4.0, 12.0 );

var skewness = beta.skewness;
// returns ~0.011

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 ~-0.207

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 ~0.013

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 = quantile( 1.9 );
// returns NaN

Examples

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

var beta = new Beta( 2.0, 4.0 );

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

var median = beta.median;
// returns ~0.313

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

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