Lévy

Lévy distribution constructor.

Usage

var Levy = require( '@stdlib/math/base/dists/levy/ctor' );

Levy( [mu, c] )

Returns a Lévy distribution object.

var levy = new Levy();

var median = levy.median;
// returns ~2.198

By default, mu = 0.0 and c = 1.0. To create a distribution having a different mu (location parameter) and c (scale parameter), provide parameter values.

var levy = new Levy( 2.0, 4.0 );

var median = levy.median;
// returns ~10.792

levy

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

Writable Properties

levy.mu

Location parameter of the distribution.

var levy = new Levy();

var mu = levy.mu;
// returns 0.0

levy.mu = 3.0;

mu = levy.mu;
// returns 3.0

levy.c

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

var levy = new Levy( 2.0, 4.0 );

var c = levy.c;
// returns 4.0

levy.c = 3.0;

c = levy.c;
// returns 3.0

Computed Properties

Levy.prototype.entropy

Returns the differential entropy.

var levy = new Levy( 4.0, 12.0 );

var entropy = levy.entropy;
// returns ~5.809

Levy.prototype.mean

Returns the expected value.

var levy = new Levy( 4.0, 12.0 );

var mu = levy.mean;
// returns Infinity

Levy.prototype.median

Returns the median.

var levy = new Levy( 4.0, 12.0 );

var median = levy.median;
// returns ~30.377

Levy.prototype.mode

Returns the mode.

var levy = new Levy( 4.0, 12.0 );

var mode = levy.mode;
// returns 8.0

Levy.prototype.stdev

Returns the standard deviation.

var levy = new Levy( 4.0, 12.0 );

var s = levy.stdev;
// returns Infinity

Levy.prototype.variance

Returns the variance.

var levy = new Levy( 4.0, 12.0 );

var s2 = levy.variance;
// returns Infinity

Methods

Levy.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var levy = new Levy( 2.0, 4.0 );

var y = levy.cdf( 2.5 );
// returns ~0.005

Levy.prototype.logcdf( x )

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

var levy = new Levy( 2.0, 4.0 );

var y = levy.logcdf( 2.5 );
// returns ~-5.3

Levy.prototype.logpdf( x )

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

var levy = new Levy( 2.0, 4.0 );

var y = levy.logpdf( 2.2 );
// returns ~-7.811

Levy.prototype.pdf( x )

Evaluates the probability density function (PDF).

var levy = new Levy( 2.0, 4.0 );

var y = levy.pdf( 2.5 );
// returns ~0.041

Levy.prototype.quantile( p )

Evaluates the quantile function at probability p.

var levy = new Levy( 2.0, 4.0 );

var y = levy.quantile( 0.5 );
// returns ~10.792

y = quantile( 1.9 );
// returns NaN

Examples

var Levy = require( '@stdlib/math/base/dists/levy/ctor' );

var levy = new Levy( 2.0, 4.0 );

var mean = levy.mean;
// returns Infinity

var median = levy.median;
// returns ~10.792

var s2 = levy.variance;
// returns Infinity

var y = levy.cdf( 20.0 );
// returns ~0.637