time-to-botec

README.md (5307B)

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 # Cauchy
 
 > Cauchy distribution constructor.
 
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 ## Usage
 
 ```javascript
 var Cauchy = require( '@stdlib/stats/base/dists/cauchy/ctor' );
 ```
 
 #### Cauchy( \[x0, gamma] )
 
 Returns a [Cauchy][cauchy-distribution] distribution object.
 
 ```javascript
 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.
 
 ```javascript
 var cauchy = new Cauchy( 2.0, 4.0 );
 
 var median = cauchy.median;
 // returns 2.0
 ```
 
 * * *
 
 ## cauchy
 
 A [Cauchy][cauchy-distribution] distribution object has the following properties and methods...
 
 ### Writable Properties
 
 #### cauchy.x0
 
 Location parameter of the distribution.
 
 ```javascript
 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.
 
 ```javascript
 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][entropy].
 
 ```javascript
 var cauchy = new Cauchy( 4.0, 12.0 );
 
 var entropy = cauchy.entropy;
 // returns ~5.016
 ```
 
 #### Cauchy.prototype.median
 
 Returns the [median][median].
 
 ```javascript
 var cauchy = new Cauchy( 4.0, 12.0 );
 
 var median = cauchy.median;
 // returns 4.0
 ```
 
 #### Cauchy.prototype.mode
 
 Returns the [mode][mode].
 
 ```javascript
 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] (CDF).
 
 ```javascript
 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] (CDF).
 
 ```javascript
 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] (PDF).
 
 ```javascript
 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] (PDF).
 
 ```javascript
 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][quantile-function] at probability `p`.
 
 ```javascript
 var cauchy = new Cauchy( 2.0, 4.0 );
 
 var y = cauchy.quantile( 0.5 );
 // returns 2.0
 
 y = cauchy.quantile( 1.9 );
 // returns NaN
 ```
 
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 * * *
 
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 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 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
 ```
 
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 [cauchy-distribution]: https://en.wikipedia.org/wiki/Cauchy_distribution
 
 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
 
 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
 
 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
 
 [entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29
 
 [median]: https://en.wikipedia.org/wiki/Median
 
 [mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29
 
 </section>
 
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