Cauchy

Cauchy distribution constructor.

Installation

npm install @stdlib/stats-base-dists-cauchy-ctor

Usage

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

Cauchy( [x0, gamma] )

Returns a Cauchy distribution object.

var cauchy = new Cauchy();

var median = cauchy.median;
// returns 0.0

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

var cauchy = new Cauchy( 2.0, 4.0 );

var median = cauchy.median;
// returns 2.0

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 = cauchy.quantile( 1.9 );
// returns NaN

Examples

var Cauchy = require( '@stdlib/stats-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

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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.