time-to-botec

README.md (6476B)

---

 <!--
 
 @license Apache-2.0
 
 Copyright (c) 2018 The Stdlib Authors.
 
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
 You may obtain a copy of the License at
 
    http://www.apache.org/licenses/LICENSE-2.0
 
 Unless required by applicable law or agreed to in writing, software
 distributed under the License is distributed on an "AS IS" BASIS,
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 
 -->
 
 # Kumaraswamy
 
 > Kumaraswamy's double bounded distribution constructor.
 
 <!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
 
 <section class="intro">
 
 </section>
 
 <!-- /.intro -->
 
 <!-- Package usage documentation. -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var Kumaraswamy = require( '@stdlib/stats/base/dists/kumaraswamy/ctor' );
 ```
 
 #### Kumaraswamy( \[a, b] )
 
 Returns a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution object.
 
 ```javascript
 var kumaraswamy = new Kumaraswamy();
 
 var mu = kumaraswamy.mean;
 // returns 0.5
 ```
 
 By default, `a = 1.0` and `b = 1.0`. To create a distribution having a different `a` (first shape parameter) and `b` (second shape parameter), provide the corresponding arguments.
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );
 
 var mu = kumaraswamy.mean;
 // returns ~0.406
 ```
 
 * * *
 
 ## kumaraswamy
 
 A [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution object has the following properties and methods...
 
 ### Writable Properties
 
 #### kumaraswamy.a
 
 First shape parameter of the distribution. `a` **must** be a positive number.
 
 ```javascript
 var kumaraswamy = new Kumaraswamy();
 
 var a = kumaraswamy.a;
 // returns 1.0
 
 kumaraswamy.a = 3.0;
 
 a = kumaraswamy.a;
 // returns 3.0
 ```
 
 #### kumaraswamy.b
 
 Second shape parameter of the distribution. `b` **must** be a positive number.
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );
 
 var b = kumaraswamy.b;
 // returns 4.0
 
 kumaraswamy.b = 3.0;
 
 b = kumaraswamy.b;
 // returns 3.0
 ```
 
 * * *
 
 ### Computed Properties
 
 #### Kumaraswamy.prototype.kurtosis
 
 Returns the [excess kurtosis][kurtosis].
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );
 
 var kurtosis = kumaraswamy.kurtosis;
 // returns ~2.704
 ```
 
 #### Kumaraswamy.prototype.mean
 
 Returns the [expected value][expected-value].
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );
 
 var mu = kumaraswamy.mean;
 // returns ~0.481
 ```
 
 #### Kumaraswamy.prototype.mode
 
 Returns the [mode][mode].
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );
 
 var mode = kumaraswamy.mode;
 // returns ~0.503
 ```
 
 #### Kumaraswamy.prototype.skewness
 
 Returns the [skewness][skewness].
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );
 
 var skewness = kumaraswamy.skewness;
 // returns ~-0.201
 ```
 
 #### Kumaraswamy.prototype.stdev
 
 Returns the [standard deviation][standard-deviation].
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );
 
 var s = kumaraswamy.stdev;
 // returns ~0.13
 ```
 
 #### Kumaraswamy.prototype.variance
 
 Returns the [variance][variance].
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );
 
 var s2 = kumaraswamy.variance;
 // returns ~0.017
 ```
 
 * * *
 
 ### Methods
 
 #### Kumaraswamy.prototype.cdf( x )
 
 Evaluates the [cumulative distribution function][cdf] (CDF).
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );
 
 var y = kumaraswamy.cdf( 0.5 );
 // returns ~0.684
 ```
 
 #### Kumaraswamy.prototype.logcdf( x )
 
 Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );
 
 var y = kumaraswamy.logcdf( 0.5 );
 // returns ~-0.38
 ```
 
 #### Kumaraswamy.prototype.logpdf( x )
 
 Evaluates the natural logarithm of the [probability density function][pdf] (PDF).
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );
 
 var y = kumaraswamy.logpdf( 0.8 );
 // returns ~-1.209
 ```
 
 #### Kumaraswamy.prototype.pdf( x )
 
 Evaluates the [probability density function][pdf] (PDF).
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );
 
 var y = kumaraswamy.pdf( 0.8 );
 // returns ~0.299
 ```
 
 #### Kumaraswamy.prototype.quantile( p )
 
 Evaluates the [quantile function][quantile-function] at probability `p`.
 
 ```javascript
 var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );
 
 var y = kumaraswamy.quantile( 0.5 );
 // returns ~0.399
 
 y = kumaraswamy.quantile( 1.9 );
 // returns NaN
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
 
 <section class="notes">
 
 </section>
 
 <!-- /.notes -->
 
 <!-- Package usage examples. -->
 
 * * *
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var Kumaraswamy = require( '@stdlib/stats/base/dists/kumaraswamy/ctor' );
 
 var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );
 
 var mu = kumaraswamy.mean;
 // returns ~0.406
 
 var mode = kumaraswamy.mode;
 // returns ~0.378
 
 var s2 = kumaraswamy.variance;
 // returns ~0.035
 
 var y = kumaraswamy.cdf( 0.8 );
 // returns ~0.983
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
 
 <section class="references">
 
 </section>
 
 <!-- /.references -->
 
 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
 
 <section class="links">
 
 [kumaraswamy-distribution]: https://en.wikipedia.org/wiki/Kumaraswamy_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>
 
 <!-- /.links -->