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# Chi

> Chi distribution constructor.

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## Usage

```javascript
var Chi = require( '@stdlib/stats/base/dists/chi/ctor' );
```

#### Chi( \[k] )

Returns an [chi][chi-distribution] distribution object.

```javascript
var chi = new Chi();

var mu = chi.mean;
// returns ~0.798
```

By default, `k = 1.0`. To create a distribution having a different degrees of freedom `k`, provide a parameter value.

```javascript
var chi = new Chi( 4.0 );

var mu = chi.mean;
// returns ~1.88
```

* * *

## chi

A [chi][chi-distribution] distribution object has the following properties and methods...

### Writable Properties

#### chi.k

Degrees of freedom of the distribution. `k` **must** be a positive number.

```javascript
var chi = new Chi( 2.0 );

var k = chi.k;
// returns 2.0

chi.k = 3.0;

k = chi.k;
// returns 3.0
```

* * *

### Computed Properties

#### Chi.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var chi = new Chi( 4.0 );

var entropy = chi.entropy;
// returns ~1.019
```

#### Chi.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var chi = new Chi( 4.0 );

var kurtosis = chi.kurtosis;
// returns ~0.059
```

#### Chi.prototype.mean

Returns the [expected value][expected-value].

```javascript
var chi = new Chi( 4.0 );

var mu = chi.mean;
// returns ~1.88
```

#### Chi.prototype.mode

Returns the [mode][mode].

```javascript
var chi = new Chi( 4.0 );

var mode = chi.mode;
// returns ~1.732
```

#### Chi.prototype.skewness

Returns the [skewness][skewness].

```javascript
var chi = new Chi( 4.0 );

var skewness = chi.skewness;
// returns ~0.406
```

#### Chi.prototype.stdev

Returns the [standard deviation][standard-deviation].

```javascript
var chi = new Chi( 4.0 );

var s = chi.stdev;
// returns ~0.682
```

#### Chi.prototype.variance

Returns the [variance][variance].

```javascript
var chi = new Chi( 4.0 );

var s2 = chi.variance;
// returns ~0.466
```

* * *

### Methods

#### Chi.prototype.cdf( x )

Evaluates the [cumulative distribution function][cdf] (CDF).

```javascript
var chi = new Chi( 2.0 );

var y = chi.cdf( 0.5 );
// returns ~0.118
```

#### Chi.prototype.logpdf( x )

Evaluates the natural logarithm of the [probability density function][pdf] (PDF).

```javascript
var chi = new Chi( 2.0 );

var y = chi.logpdf( 0.8 );
// returns ~-0.543
```

#### Chi.prototype.pdf( x )

Evaluates the [probability density function][pdf] (PDF).

```javascript
var chi = new Chi( 2.0 );

var y = chi.pdf( 0.8 );
// returns ~0.581
```

#### Chi.prototype.quantile( p )

Evaluates the [quantile function][quantile-function] at probability `p`.

```javascript
var chi = new Chi( 2.0 );

var y = chi.quantile( 0.5 );
// returns ~1.177

y = chi.quantile( 1.9 );
// returns NaN
```

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* * *

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var Chi = require( '@stdlib/stats/base/dists/chi/ctor' );

var chi = new Chi( 2.0 );

var mu = chi.mean;
// returns ~1.253

var mode = chi.mode;
// returns 1.0

var s2 = chi.variance;
// returns ~0.429

var y = chi.cdf( 0.8 );
// returns ~0.274
```

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[chi-distribution]: https://en.wikipedia.org/wiki/Chi_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

[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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