# Cauchy

Cauchy distribution constructor.

## 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
``````