time-to-botec

README.md (6326B)

---

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 # Beta Prime
 
 > Beta prime distribution constructor.
 
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 ## Usage
 
 ```javascript
 var BetaPrime = require( '@stdlib/stats/base/dists/betaprime/ctor' );
 ```
 
 #### BetaPrime( \[alpha, beta] )
 
 Returns a [beta prime][betaprime-distribution] distribution object.
 
 ```javascript
 var betaprime = new BetaPrime();
 
 var mode = betaprime.mode;
 // returns 0.0
 ```
 
 By default, `alpha = 1.0` and `beta = 1.0`. To create a distribution having a different `alpha` (first shape parameter) and `beta` (second shape parameter), provide the corresponding arguments.
 
 ```javascript
 var betaprime = new BetaPrime( 2.0, 4.0 );
 
 var mu = betaprime.mean;
 // returns ~0.667
 ```
 
 * * *
 
 ## betaprime
 
 A [beta prime][betaprime-distribution] distribution object has the following properties and methods...
 
 ### Writable Properties
 
 #### betaprime.alpha
 
 First shape parameter of the distribution. `alpha` **must** be a positive number.
 
 ```javascript
 var betaprime = new BetaPrime();
 
 var alpha = betaprime.alpha;
 // returns 1.0
 
 betaprime.alpha = 3.0;
 
 alpha = betaprime.alpha;
 // returns 3.0
 ```
 
 #### betaprime.beta
 
 Second shape parameter of the distribution. `beta` **must** be a positive number.
 
 ```javascript
 var betaprime = new BetaPrime( 2.0, 4.0 );
 
 var b = betaprime.beta;
 // returns 4.0
 
 betaprime.beta = 3.0;
 
 b = betaprime.beta;
 // returns 3.0
 ```
 
 * * *
 
 ### Computed Properties
 
 #### BetaPrime.prototype.kurtosis
 
 Returns the [excess kurtosis][kurtosis].
 
 ```javascript
 var betaprime = new BetaPrime( 4.0, 12.0 );
 
 var kurtosis = betaprime.kurtosis;
 // returns ~5.764
 ```
 
 #### BetaPrime.prototype.mean
 
 Returns the [expected value][expected-value].
 
 ```javascript
 var betaprime = new BetaPrime( 4.0, 12.0 );
 
 var mu = betaprime.mean;
 // returns ~0.364
 ```
 
 #### BetaPrime.prototype.mode
 
 Returns the [mode][mode].
 
 ```javascript
 var betaprime = new BetaPrime( 4.0, 12.0 );
 
 var mode = betaprime.mode;
 // returns ~0.231
 ```
 
 #### BetaPrime.prototype.skewness
 
 Returns the [skewness][skewness].
 
 ```javascript
 var betaprime = new BetaPrime( 4.0, 12.0 );
 
 var skewness = betaprime.skewness;
 // returns ~1.724
 ```
 
 #### BetaPrime.prototype.stdev
 
 Returns the [standard deviation][standard-deviation].
 
 ```javascript
 var betaprime = new BetaPrime( 4.0, 12.0 );
 
 var s = betaprime.stdev;
 // returns ~0.223
 ```
 
 #### BetaPrime.prototype.variance
 
 Returns the [variance][variance].
 
 ```javascript
 var betaprime = new BetaPrime( 4.0, 12.0 );
 
 var s2 = betaprime.variance;
 // returns ~0.05
 ```
 
 * * *
 
 ### Methods
 
 #### BetaPrime.prototype.cdf( x )
 
 Evaluates the [cumulative distribution function][cdf] (CDF).
 
 ```javascript
 var betaprime = new BetaPrime( 2.0, 4.0 );
 
 var y = betaprime.cdf( 0.5 );
 // returns ~0.539
 ```
 
 #### BetaPrime.prototype.logcdf( x )
 
 Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).
 
 ```javascript
 var betaprime = new BetaPrime( 2.0, 4.0 );
 
 var y = betaprime.logcdf( 0.5 );
 // returns ~-0.618
 ```
 
 #### BetaPrime.prototype.logpdf( x )
 
 Evaluates the natural logarithm of the [probability density function][pdf] (PDF).
 
 ```javascript
 var betaprime = new BetaPrime( 2.0, 4.0 );
 
 var y = betaprime.logpdf( 0.8 );
 // returns ~-0.754
 ```
 
 #### BetaPrime.prototype.pdf( x )
 
 Evaluates the [probability density function][pdf] (PDF).
 
 ```javascript
 var betaprime = new BetaPrime( 2.0, 4.0 );
 
 var y = betaprime.pdf( 0.8 );
 // returns ~0.47
 ```
 
 #### BetaPrime.prototype.quantile( p )
 
 Evaluates the [quantile function][quantile-function] at probability `p`.
 
 ```javascript
 var betaprime = new BetaPrime( 2.0, 4.0 );
 
 var y = betaprime.quantile( 0.5 );
 // returns ~0.457
 
 y = betaprime.quantile( 1.9 );
 // returns NaN
 ```
 
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 * * *
 
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 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var BetaPrime = require( '@stdlib/stats/base/dists/betaprime/ctor' );
 
 var betaprime = new BetaPrime( 2.0, 4.0 );
 
 var mu = betaprime.mean;
 // returns ~0.667
 
 var mode = betaprime.mode;
 // returns 0.2
 
 var s2 = betaprime.variance;
 // returns ~0.556
 
 var y = betaprime.cdf( 0.8 );
 // returns ~0.735
 ```
 
 </section>
 
 <!-- /.examples -->
 
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 [betaprime-distribution]: https://en.wikipedia.org/wiki/Beta_prime_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
 
 [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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