time-to-botec

README.md (5851B)

---

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 # Lévy
 
 > Lévy distribution constructor.
 
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 ## Usage
 
 ```javascript
 var Levy = require( '@stdlib/stats/base/dists/levy/ctor' );
 ```
 
 #### Levy( \[mu, c] )
 
 Returns a [Lévy][levy-distribution] distribution object.
 
 ```javascript
 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 the corresponding arguments.
 
 ```javascript
 var levy = new Levy( 2.0, 4.0 );
 
 var median = levy.median;
 // returns ~10.792
 ```
 
 * * *
 
 ## levy
 
 A [Lévy][levy-distribution] distribution object has the following properties and methods...
 
 ### Writable Properties
 
 #### levy.mu
 
 Location parameter of the distribution.
 
 ```javascript
 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.
 
 ```javascript
 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][entropy].
 
 ```javascript
 var levy = new Levy( 4.0, 12.0 );
 
 var entropy = levy.entropy;
 // returns ~5.809
 ```
 
 #### Levy.prototype.mean
 
 Returns the [expected value][expected-value].
 
 ```javascript
 var levy = new Levy( 4.0, 12.0 );
 
 var mu = levy.mean;
 // returns Infinity
 ```
 
 #### Levy.prototype.median
 
 Returns the [median][median].
 
 ```javascript
 var levy = new Levy( 4.0, 12.0 );
 
 var median = levy.median;
 // returns ~30.377
 ```
 
 #### Levy.prototype.mode
 
 Returns the [mode][mode].
 
 ```javascript
 var levy = new Levy( 4.0, 12.0 );
 
 var mode = levy.mode;
 // returns 8.0
 ```
 
 #### Levy.prototype.stdev
 
 Returns the [standard deviation][standard-deviation].
 
 ```javascript
 var levy = new Levy( 4.0, 12.0 );
 
 var s = levy.stdev;
 // returns Infinity
 ```
 
 #### Levy.prototype.variance
 
 Returns the [variance][variance].
 
 ```javascript
 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] (CDF).
 
 ```javascript
 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] (CDF).
 
 ```javascript
 var levy = new Levy( 2.0, 4.0 );
 
 var y = levy.logcdf( 2.5 );
 // returns ~-5.365
 ```
 
 #### Levy.prototype.logpdf( x )
 
 Evaluates the natural logarithm of the [probability density function][pdf] (PDF).
 
 ```javascript
 var levy = new Levy( 2.0, 4.0 );
 
 var y = levy.logpdf( 2.2 );
 // returns ~-7.812
 ```
 
 #### Levy.prototype.pdf( x )
 
 Evaluates the [probability density function][pdf] (PDF).
 
 ```javascript
 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][quantile-function] at probability `p`.
 
 ```javascript
 var levy = new Levy( 2.0, 4.0 );
 
 var y = levy.quantile( 0.5 );
 // returns ~10.792
 
 y = levy.quantile( 1.9 );
 // returns NaN
 ```
 
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 * * *
 
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 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var Levy = require( '@stdlib/stats/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
 ```
 
 </section>
 
 <!-- /.examples -->
 
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 <section class="links">
 
 [levy-distribution]: https://en.wikipedia.org/wiki/L%C3%A9vy_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
 
 [expected-value]: https://en.wikipedia.org/wiki/Expected_value
 
 [median]: https://en.wikipedia.org/wiki/Median
 
 [mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29
 
 [standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation
 
 [variance]: https://en.wikipedia.org/wiki/Variance
 
 </section>
 
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