time-to-botec

README.md (6278B)

---

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 # Erlang
 
 > Erlang distribution constructor.
 
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 ## Usage
 
 ```javascript
 var Erlang = require( '@stdlib/stats/base/dists/erlang/ctor' );
 ```
 
 #### Erlang( \[k, lambda] )
 
 Returns an [Erlang][erlang-distribution] distribution object.
 
 ```javascript
 var erlang = new Erlang();
 
 var mode = erlang.mode;
 // returns 0.0
 ```
 
 By default, `k = 1.0` and `lambda = 1.0`. To create a distribution having a different `k` (shape parameter) and `lambda` (rate parameter), provide the corresponding arguments.
 
 ```javascript
 var erlang = new Erlang( 2, 4.0 );
 
 var mode = erlang.mode;
 // returns 0.25
 ```
 
 * * *
 
 ## erlang
 
 An [Erlang][erlang-distribution] distribution object has the following properties and methods...
 
 ### Writable Properties
 
 #### erlang.k
 
 Shape parameter of the distribution. `k` **must** be a positive integer.
 
 ```javascript
 var erlang = new Erlang();
 
 var k = erlang.k;
 // returns 1.0
 
 erlang.k = 3.0;
 
 k = erlang.k;
 // returns 3.0
 ```
 
 #### erlang.lambda
 
 Rate parameter of the distribution. `lambda` **must** be a positive number.
 
 ```javascript
 var erlang = new Erlang( 2, 4.0 );
 
 var lambda = erlang.lambda;
 // returns 4.0
 
 erlang.lambda = 3.0;
 
 lambda = erlang.lambda;
 // returns 3.0
 ```
 
 * * *
 
 ### Computed Properties
 
 #### Erlang.prototype.entropy
 
 Returns the [differential entropy][entropy].
 
 ```javascript
 var erlang = new Erlang( 4, 12.0 );
 
 var entropy = erlang.entropy;
 // returns ~-0.462
 ```
 
 #### Erlang.prototype.kurtosis
 
 Returns the [excess kurtosis][kurtosis].
 
 ```javascript
 var erlang = new Erlang( 4, 12.0 );
 
 var kurtosis = erlang.kurtosis;
 // returns 1.5
 ```
 
 #### Erlang.prototype.mean
 
 Returns the [expected value][expected-value].
 
 ```javascript
 var erlang = new Erlang( 4, 12.0 );
 
 var mu = erlang.mean;
 // returns ~0.333
 ```
 
 #### Erlang.prototype.mode
 
 Returns the [mode][mode].
 
 ```javascript
 var erlang = new Erlang( 4, 12.0 );
 
 var mode = erlang.mode;
 // returns 0.25
 ```
 
 #### Erlang.prototype.skewness
 
 Returns the [skewness][skewness].
 
 ```javascript
 var erlang = new Erlang( 4, 12.0 );
 
 var skewness = erlang.skewness;
 // returns 1.0
 ```
 
 #### Erlang.prototype.stdev
 
 Returns the [standard deviation][standard-deviation].
 
 ```javascript
 var erlang = new Erlang( 4, 12.0 );
 
 var s = erlang.stdev;
 // returns ~0.167
 ```
 
 #### Erlang.prototype.variance
 
 Returns the [variance][variance].
 
 ```javascript
 var erlang = new Erlang( 4, 12.0 );
 
 var s2 = erlang.variance;
 // returns ~0.028
 ```
 
 * * *
 
 ### Methods
 
 #### Erlang.prototype.cdf( x )
 
 Evaluates the [cumulative distribution function][cdf] (CDF).
 
 ```javascript
 var erlang = new Erlang( 2, 4.0 );
 
 var y = erlang.cdf( 0.5 );
 // returns ~0.594
 ```
 
 #### Erlang.prototype.logpdf( x )
 
 Evaluates the natural logarithm of the [probability density function][pdf] (PDF).
 
 ```javascript
 var erlang = new Erlang( 2, 4.0 );
 
 var y = erlang.logpdf( 0.8 );
 // returns ~-0.65
 ```
 
 #### Erlang.prototype.mgf( t )
 
 Evaluates the [moment-generating function][mgf] (MGF).
 
 ```javascript
 var erlang = new Erlang( 2, 4.0 );
 
 var y = erlang.mgf( 0.5 );
 // returns ~1.306
 ```
 
 #### Erlang.prototype.pdf( x )
 
 Evaluates the [probability density function][pdf] (PDF).
 
 ```javascript
 var erlang = new Erlang( 2, 4.0 );
 
 var y = erlang.pdf( 0.8 );
 // returns ~0.522
 ```
 
 #### Erlang.prototype.quantile( p )
 
 Evaluates the [quantile function][quantile-function] at probability `p`.
 
 ```javascript
 var erlang = new Erlang( 2, 4.0 );
 
 var y = erlang.quantile( 0.5 );
 // returns ~0.42
 
 y = erlang.quantile( 1.9 );
 // returns NaN
 ```
 
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 * * *
 
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 ## Examples
 
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 ```javascript
 var Erlang = require( '@stdlib/stats/base/dists/erlang/ctor' );
 
 var erlang = new Erlang( 2, 4.0 );
 
 var mu = erlang.mean;
 // returns 0.5
 
 var mode = erlang.mode;
 // returns 0.25
 
 var s2 = erlang.variance;
 // returns 0.125
 
 var y = erlang.cdf( 0.8 );
 // returns ~0.829
 ```
 
 </section>
 
 <!-- /.examples -->
 
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 [erlang-distribution]: https://en.wikipedia.org/wiki/Erlang_distribution
 
 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
 
 [mgf]: https://en.wikipedia.org/wiki/Moment-generating_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
 
 [kurtosis]: https://en.wikipedia.org/wiki/Kurtosis
 
 [mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29
 
 [skewness]: https://en.wikipedia.org/wiki/Skewness
 
 [standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation
 
 [variance]: https://en.wikipedia.org/wiki/Variance
 
 </section>
 
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