Beta Prime

Beta prime distribution constructor.

Usage

var BetaPrime = require( '@stdlib/math/base/dists/betaprime/ctor' );

BetaPrime( [alpha, beta] )

Returns a beta prime distribution object.

var betaprime = new BetaPrime();

var mode = betaprime.mode;
// returns 0.0

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 betaprime = new BetaPrime( 2.0, 4.0 );

var mu = betaprime.mean;
// returns ~0.667

betaprime

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

Writable Properties

betaprime.alpha

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

var betaprime = new BetaPrime();

var alpha = betaprime.alpha;
// returns 1.0

betaprime.alpha = 3.0;

alpha = betaprime.alpha;
// returns 3.0

betaprime.beta

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

var betaprime = new BetaPrime( 2.0, 4.0 );

var b = betaprime.beta;
// returns 4.0

betaprime.beta = 3.0;

b = betaprime.beta;
// returns 3.0

Computed Properties

BetaPrime.prototype.kurtosis

Returns the excess kurtosis.

var betaprime = new BetaPrime( 4.0, 12.0 );

var kurtosis = betaprime.kurtosis;
// returns ~5.764

BetaPrime.prototype.mean

Returns the expected value.

var betaprime = new BetaPrime( 4.0, 12.0 );

var mu = betaprime.mean;
// returns ~0.364

BetaPrime.prototype.mode

Returns the mode.

var betaprime = new BetaPrime( 4.0, 12.0 );

var mode = betaprime.mode;
// returns ~0.231

BetaPrime.prototype.skewness

Returns the skewness.

var betaprime = new BetaPrime( 4.0, 12.0 );

var skewness = betaprime.skewness;
// returns ~1.724

BetaPrime.prototype.stdev

Returns the standard deviation.

var betaprime = new BetaPrime( 4.0, 12.0 );

var s = betaprime.stdev;
// returns ~0.224

BetaPrime.prototype.variance

Returns the variance.

var betaprime = new BetaPrime( 4.0, 12.0 );

var s2 = betaprime.variance;
// returns ~0.05

Methods

BetaPrime.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.cdf( 0.5 );
// returns ~0.539

BetaPrime.prototype.logcdf( x )

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

var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.logcdf( 0.5 );
// returns ~-0.618

BetaPrime.prototype.logpdf( x )

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

var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.logpdf( 0.8 );
// returns ~-0.751

BetaPrime.prototype.pdf( x )

Evaluates the probability density function (PDF).

var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.pdf( 0.8 );
// returns ~0.47

BetaPrime.prototype.quantile( p )

Evaluates the quantile function at probability p.

var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.quantile( 0.5 );
// returns ~0.457

y = quantile( 1.9 );
// returns NaN

Examples

var BetaPrime = require( '@stdlib/math/base/dists/betaprime/ctor' );

var betaprime = new BetaPrime( 2.0, 4.0 );

var mu = betaprime.mean;
// returns ~0.667

var mode = betaprime.mode;
// returns 0.2

var s2 = betaprime.variance;
// returns ~0.556

var y = betaprime.cdf( 0.8 );
// returns ~0.735