@stdlib/stats/base/dists/chisquare/ctor/README.md

Standard library statistical functions.

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# ChiSquare

> Chi-squared distribution constructor.

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## 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
```

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* * *

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## Examples

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```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
```

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[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

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