# ChiSquare
> Chi-squared distribution constructor.
## Usage
```javascript
var ChiSquare = require( '@stdlib/stats/base/dists/chisquare/ctor' );
```
#### ChiSquare( \[k] )
Returns an [chi-squared][chisquare-distribution] distribution object.
```javascript
var chisquare = new ChiSquare();
var mu = chisquare.mean;
// returns 1.0
```
By default, `k = 1.0`. To create a distribution having a different degrees of freedom `k`, provide a parameter value.
```javascript
var chisquare = new ChiSquare( 4.0 );
var mu = chisquare.mean;
// returns 4.0
```
* * *
## chisquare
A [chi-squared][chisquare-distribution] distribution object has the following properties and methods...
### Writable Properties
#### chisquare.k
Rate parameter of the distribution. `k` **must** be a positive number.
```javascript
var chisquare = new ChiSquare( 2.0 );
var k = chisquare.k;
// returns 2.0
chisquare.k = 3.0;
k = chisquare.k;
// returns 3.0
```
* * *
### Computed Properties
#### ChiSquare.prototype.entropy
Returns the [differential entropy][entropy].
```javascript
var chisquare = new ChiSquare( 4.0 );
var entropy = chisquare.entropy;
// returns ~2.27
```
#### ChiSquare.prototype.kurtosis
Returns the [excess kurtosis][kurtosis].
```javascript
var chisquare = new ChiSquare( 4.0 );
var kurtosis = chisquare.kurtosis;
// returns 3.0
```
#### ChiSquare.prototype.mean
Returns the [expected value][expected-value].
```javascript
var chisquare = new ChiSquare( 4.0 );
var mu = chisquare.mean;
// returns 4.0
```
#### ChiSquare.prototype.median
Returns the [median][median].
```javascript
var chisquare = new ChiSquare( 4.0 );
var median = chisquare.median;
// returns ~3.357
```
#### ChiSquare.prototype.mode
Returns the [mode][mode].
```javascript
var chisquare = new ChiSquare( 4.0 );
var mode = chisquare.mode;
// returns 2.0
```
#### ChiSquare.prototype.skewness
Returns the [skewness][skewness].
```javascript
var chisquare = new ChiSquare( 4.0 );
var skewness = chisquare.skewness;
// returns ~1.414
```
#### ChiSquare.prototype.stdev
Returns the [standard deviation][standard-deviation].
```javascript
var chisquare = new ChiSquare( 4.0 );
var s = chisquare.stdev;
// returns ~2.828
```
#### ChiSquare.prototype.variance
Returns the [variance][variance].
```javascript
var chisquare = new ChiSquare( 4.0 );
var s2 = chisquare.variance;
// returns 8.0
```
* * *
### Methods
#### ChiSquare.prototype.cdf( x )
Evaluates the [cumulative distribution function][cdf] (CDF).
```javascript
var chisquare = new ChiSquare( 2.0 );
var y = chisquare.cdf( 0.5 );
// returns ~0.221
```
#### ChiSquare.prototype.mgf( t )
Evaluates the [moment-generating function][mgf] (MGF).
```javascript
var chisquare = new ChiSquare( 2.0 );
var y = chisquare.mgf( 0.2 );
// returns ~1.667
```
#### ChiSquare.prototype.pdf( x )
Evaluates the [probability density function][pdf] (PDF).
```javascript
var chisquare = new ChiSquare( 2.0 );
var y = chisquare.pdf( 0.8 );
// returns ~0.335
```
#### ChiSquare.prototype.quantile( p )
Evaluates the [quantile function][quantile-function] at probability `p`.
```javascript
var chisquare = new ChiSquare( 2.0 );
var y = chisquare.quantile( 0.5 );
// returns ~1.386
y = chisquare.quantile( 1.9 );
// returns NaN
```
* * *
## Examples
```javascript
var ChiSquare = require( '@stdlib/stats/base/dists/chisquare/ctor' );
var chisquare = new ChiSquare( 2.0 );
var mu = chisquare.mean;
// returns 2.0
var mode = chisquare.mode;
// returns 0.0
var s2 = chisquare.variance;
// returns 4.0
var y = chisquare.cdf( 0.8 );
// returns ~0.33
```
[chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_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
[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