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

Standard library statistical functions.

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# Normal

> Normal distribution constructor.

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## Usage

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

#### Normal( \[mu, sigma] )

Returns a [normal][normal-distribution] distribution object.

```javascript
var normal = new Normal();

var mu = normal.mean;
// returns 0.0
```

By default, `mu = 0.0` and `sigma = 1.0`. To create a distribution having a different `mu` (mean parameter) and `sigma` (standard deviation), provide the corresponding arguments.

```javascript
var normal = new Normal( 2.0, 4.0 );

var mu = normal.mean;
// returns 2.0
```

* * *

## normal

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

### Writable Properties

#### normal.mu

Mean parameter of the distribution.

```javascript
var normal = new Normal();

var mu = normal.mu;
// returns 0.0

normal.mu = 3.0;

mu = normal.mu;
// returns 3.0
```

#### normal.sigma

Standard deviation of the distribution. `sigma` **must** be a positive number.

```javascript
var normal = new Normal( 2.0, 4.0 );

var sigma = normal.sigma;
// returns 4.0

normal.sigma = 3.0;

sigma = normal.sigma;
// returns 3.0
```

* * *

### Computed Properties

#### Normal.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var normal = new Normal( 4.0, 12.0 );

var entropy = normal.entropy;
// returns ~3.904
```

#### Normal.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var normal = new Normal( 4.0, 12.0 );

var kurtosis = normal.kurtosis;
// returns 0.0
```

#### Normal.prototype.mean

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

```javascript
var normal = new Normal( 4.0, 12.0 );

var mu = normal.mean;
// returns 4.0
```

#### Normal.prototype.median

Returns the [median][median].

```javascript
var normal = new Normal( 4.0, 12.0 );

var median = normal.median;
// returns 4.0
```

#### Normal.prototype.mode

Returns the [mode][mode].

```javascript
var normal = new Normal( 4.0, 12.0 );

var mode = normal.mode;
// returns 4.0
```

#### Normal.prototype.skewness

Returns the [skewness][skewness].

```javascript
var normal = new Normal( 4.0, 12.0 );

var skewness = normal.skewness;
// returns 0.0
```

#### Normal.prototype.stdev

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

```javascript
var normal = new Normal( 4.0, 12.0 );

var s = normal.stdev;
// returns 12.0
```

#### Normal.prototype.variance

Returns the [variance][variance].

```javascript
var normal = new Normal( 4.0, 12.0 );

var s2 = normal.variance;
// returns 144.0
```

* * *

### Methods

#### Normal.prototype.cdf( x )

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

```javascript
var normal = new Normal( 2.0, 4.0 );

var y = normal.cdf( 0.5 );
// returns ~0.354
```

#### Normal.prototype.logcdf( x )

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

```javascript
var normal = new Normal( 2.0, 4.0 );

var y = normal.logcdf( 0.5 );
// returns ~-1.039
```

#### Normal.prototype.logpdf( x )

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

```javascript
var normal = new Normal( 2.0, 4.0 );

var y = normal.logpdf( 2.0 );
// returns ~-2.305
```

#### Normal.prototype.mgf( t )

Evaluates the [moment-generating function][mgf] (MGF).

```javascript
var normal = new Normal( 2.0, 4.0 );

var y = normal.mgf( 0.2 );
// returns ~2.054
```

#### Normal.prototype.pdf( x )

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

```javascript
var normal = new Normal( 2.0, 4.0 );

var y = normal.pdf( 2.0 );
// returns ~0.1
```

#### Normal.prototype.quantile( p )

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

```javascript
var normal = new Normal( 2.0, 4.0 );

var y = normal.quantile( 0.5 );
// returns 2.0

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

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* * *

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## Examples

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

var normal = new Normal( 2.0, 4.0 );

var mean = normal.mean;
// returns 2.0

var median = normal.median;
// returns 2.0

var s2 = normal.variance;
// returns 16.0

var y = normal.cdf( 0.8 );
// returns ~0.382
```

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[normal-distribution]: https://en.wikipedia.org/wiki/Normal_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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