time-to-botec

README.md (5708B)

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 # Student's T
 
 > Student's t distribution constructor.
 
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 ## Usage
 
 ```javascript
 var T = require( '@stdlib/stats/base/dists/t/ctor' );
 ```
 
 #### T( \[v] )
 
 Returns a [Student's t][t-distribution] distribution object.
 
 ```javascript
 var t = new T();
 
 var mu = t.mean;
 // returns NaN
 ```
 
 By default, `v = 1.0`. To create a distribution having a different degrees of freedom `v`, provide a parameter value.
 
 ```javascript
 var t = new T( 4.0 );
 
 var mu = t.mean;
 // returns 0.0
 ```
 
 * * *
 
 ## t
 
 A [Student's t][t-distribution] distribution object has the following properties and methods...
 
 ### Writable Properties
 
 #### t.v
 
 Degrees of freedom of the distribution. `v` **must** be a positive number.
 
 ```javascript
 var t = new T( 2.0 );
 
 var v = t.v;
 // returns 2.0
 
 t.v = 3.0;
 
 v = t.v;
 // returns 3.0
 ```
 
 * * *
 
 ### Computed Properties
 
 #### T.prototype.entropy
 
 Returns the [differential entropy][entropy].
 
 ```javascript
 var t = new T( 4.0 );
 
 var entropy = t.entropy;
 // returns ~1.682
 ```
 
 #### T.prototype.kurtosis
 
 Returns the [excess kurtosis][kurtosis].
 
 ```javascript
 var t = new T( 4.0 );
 
 var kurtosis = t.kurtosis;
 // returns Infinity
 ```
 
 #### T.prototype.mean
 
 Returns the [expected value][expected-value].
 
 ```javascript
 var t = new T( 4.0 );
 
 var mu = t.mean;
 // returns 0.0
 ```
 
 #### T.prototype.median
 
 Returns the [median][median].
 
 ```javascript
 var t = new T( 4.0 );
 
 var median = t.median;
 // returns 0.0
 ```
 
 #### T.prototype.mode
 
 Returns the [mode][mode].
 
 ```javascript
 var t = new T( 4.0 );
 
 var mode = t.mode;
 // returns 0.0
 ```
 
 #### T.prototype.skewness
 
 Returns the [skewness][skewness].
 
 ```javascript
 var t = new T( 4.0 );
 
 var skewness = t.skewness;
 // returns 0.0
 ```
 
 #### T.prototype.stdev
 
 Returns the [standard deviation][standard-deviation].
 
 ```javascript
 var t = new T( 4.0 );
 
 var s = t.stdev;
 // returns ~1.414
 ```
 
 #### T.prototype.variance
 
 Returns the [variance][variance].
 
 ```javascript
 var t = new T( 4.0 );
 
 var s2 = t.variance;
 // returns 2.0
 ```
 
 * * *
 
 ### Methods
 
 #### T.prototype.cdf( x )
 
 Evaluates the [cumulative distribution function][cdf] (CDF).
 
 ```javascript
 var t = new T( 2.0 );
 
 var y = t.cdf( 0.5 );
 // returns ~0.667
 ```
 
 #### T.prototype.logcdf( x )
 
 Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).
 
 ```javascript
 var t = new T( 2.0 );
 
 var y = t.logcdf( 0.5 );
 // returns ~-0.405
 ```
 
 #### T.prototype.logpdf( x )
 
 Evaluates the natural logarithm of the [probability density function][pdf] (PDF).
 
 ```javascript
 var t = new T( 2.0 );
 
 var y = t.logpdf( 0.8 );
 // returns ~-1.456
 ```
 
 #### T.prototype.pdf( x )
 
 Evaluates the [probability density function][pdf] (PDF).
 
 ```javascript
 var t = new T( 2.0 );
 
 var y = t.pdf( 0.8 );
 // returns ~0.233
 ```
 
 #### T.prototype.quantile( p )
 
 Evaluates the [quantile function][quantile-function] at probability `p`.
 
 ```javascript
 var t = new T( 2.0 );
 
 var y = t.quantile( 0.5 );
 // returns 0.0
 
 y = t.quantile( 1.9 );
 // returns NaN
 ```
 
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 * * *
 
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 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var T = require( '@stdlib/stats/base/dists/t/ctor' );
 
 var t = new T( 2.0 );
 
 var mu = t.mean;
 // returns 0.0
 
 var mode = t.mode;
 // returns 0.0
 
 var s2 = t.variance;
 // returns Infinity
 
 var y = t.cdf( 0.8 );
 // returns ~0.746
 ```
 
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 <section class="links">
 
 [t-distribution]: https://en.wikipedia.org/wiki/Student%27s_t-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
 
 [kurtosis]: https://en.wikipedia.org/wiki/Kurtosis
 
 [median]: https://en.wikipedia.org/wiki/Median
 
 [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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