Cauchy

Cauchy distribution constructor.

Usage

var Cauchy = require( '@stdlib/math/base/dists/cauchy/ctor' );

Cauchy( [x0, gamma] )

Returns a Cauchy distribution object.

var cauchy = new Cauchy();

var median = cauchy.median;
// returns 0.5

By default, x0 = 0.0 and gamma = 1.0. To create a distribution having a different x0 (location parameter) and gamma (scale parameter), provide parameter values.

var cauchy = new Cauchy( 2.0, 4.0 );

var median = cauchy.median;
// returns ~0.333

cauchy

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

Writable Properties

cauchy.x0

Location parameter of the distribution.

var cauchy = new Cauchy();

var x0 = cauchy.x0;
// returns 0.0

cauchy.x0 = 3.0;

x0 = cauchy.x0;
// returns 3.0

cauchy.gamma

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

var cauchy = new Cauchy( 2.0, 4.0 );

var gamma = cauchy.gamma;
// returns 4.0

cauchy.gamma = 3.0;

gamma = cauchy.gamma;
// returns 3.0

Computed Properties

Cauchy.prototype.entropy

Returns the differential entropy.

var cauchy = new Cauchy( 4.0, 12.0 );

var entropy = cauchy.entropy;
// returns ~5.016

Cauchy.prototype.median

Returns the median.

var cauchy = new Cauchy( 4.0, 12.0 );

var median = cauchy.median;
// returns 4.0

Cauchy.prototype.mode

Returns the mode.

var cauchy = new Cauchy( 4.0, 12.0 );

var mode = cauchy.mode;
// returns 4.0

Methods

Cauchy.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var cauchy = new Cauchy( 2.0, 4.0 );

var y = cauchy.cdf( 0.5 );
// returns ~0.386

Cauchy.prototype.logcdf( x )

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

var cauchy = new Cauchy( 2.0, 4.0 );

var y = cauchy.logcdf( 0.5 );
// returns ~-0.952

Cauchy.prototype.logpdf( x )

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

var cauchy = new Cauchy( 2.0, 4.0 );

var y = cauchy.logpdf( 0.8 );
// returns ~-2.617

Cauchy.prototype.pdf( x )

Evaluates the probability density function (PDF).

var cauchy = new Cauchy( 2.0, 4.0 );

var y = cauchy.pdf( 0.8 );
// returns ~0.073

Cauchy.prototype.quantile( p )

Evaluates the quantile function at probability p.

var cauchy = new Cauchy( 2.0, 4.0 );

var y = cauchy.quantile( 0.5 );
// returns 2.0

y = quantile( 1.9 );
// returns NaN

Examples

var Cauchy = require( '@stdlib/math/base/dists/cauchy/ctor' );

var cauchy = new Cauchy( 2.0, 4.0 );

var entropy = cauchy.entropy;
// returns ~3.917

var median = cauchy.median;
// returns 2.0

var mode = cauchy.mode;
// returns 2.0

var y = cauchy.cdf( 0.8 );
// returns ~0.407