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

Standard library statistical functions.

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# Triangular

> Triangular distribution constructor.

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## Usage

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

#### Triangular( \[a, b, c] )

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

```javascript
var triangular = new Triangular();

var mu = triangular.mean;
// returns 0.5
```

By default, `a = 0.0`, `b = 1.0`, and `c = 0.5`. To create a distribution having a different `a` (minimum support), `b` (maximum support), and `c` (mode), provide the corresponding arguments.

```javascript
var triangular = new Triangular( 2.0, 4.0, 3.5 );

var mu = triangular.mean;
// returns ~3.167
```

* * *

## triangular

An [triangular][triangular-distribution] distribution object has the following properties and methods...

### Writable Properties

#### triangular.a

Minimum support of the distribution. `a` **must** be a number smaller than or equal to `b` and `c`.

```javascript
var triangular = new Triangular();

var a = triangular.a;
// returns 0.0

triangular.a = 0.5;

a = triangular.a;
// returns 0.5
```

#### triangular.b

Maximum support of the distribution. `b` **must** be a number larger than or equal to `a` and `c`.

```javascript
var triangular = new Triangular( 2.0, 4.0, 2.5 );

var b = triangular.b;
// returns 4.0

triangular.b = 3.0;

b = triangular.b;
// returns 3.0
```

#### triangular.c

Mode of the distribution. `c` **must** be a number larger than or equal to `a` and smaller than or equal to `b`.

```javascript
var triangular = new Triangular( 2.0, 5.0, 4.0 );

var c = triangular.c;
// returns 4.0

triangular.c = 3.0;

c = triangular.c;
// returns 3.0
```

* * *

### Computed Properties

#### Triangular.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var triangular = new Triangular( 4.0, 12.0, 10.0 );

var entropy = triangular.entropy;
// returns ~1.886
```

#### Triangular.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var triangular = new Triangular( 4.0, 12.0, 10.0 );

var kurtosis = triangular.kurtosis;
// returns -0.6
```

#### Triangular.prototype.mean

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

```javascript
var triangular = new Triangular( 4.0, 12.0, 10.0 );

var mu = triangular.mean;
// returns ~8.667
```

#### Triangular.prototype.median

Returns the [median][median].

```javascript
var triangular = new Triangular( 4.0, 12.0, 10.0 );

var median = triangular.median;
// returns ~8.899
```

#### Triangular.prototype.mode

Returns the [mode][mode].

```javascript
var triangular = new Triangular( 4.0, 12.0, 10.0 );

var mode = triangular.mode;
// returns 10.0
```

#### Triangular.prototype.skewness

Returns the [skewness][skewness].

```javascript
var triangular = new Triangular( 4.0, 12.0, 10.0 );

var skewness = triangular.skewness;
// returns ~-0.422
```

#### Triangular.prototype.stdev

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

```javascript
var triangular = new Triangular( 4.0, 12.0, 10.0 );

var s = triangular.stdev;
// returns ~1.7
```

#### Triangular.prototype.variance

Returns the [variance][variance].

```javascript
var triangular = new Triangular( 4.0, 12.0, 10.0 );

var s2 = triangular.variance;
// returns ~2.889
```

* * *

### Methods

#### Triangular.prototype.cdf( x )

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

```javascript
var triangular = new Triangular( 2.0, 4.0, 3.0 );

var y = triangular.cdf( 2.5 );
// returns 0.125
```

#### Triangular.prototype.logcdf( x )

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

```javascript
var triangular = new Triangular( 2.0, 4.0, 3.0 );

var y = triangular.logcdf( 2.5 );
// returns ~-2.079
```

#### Triangular.prototype.logpdf( x )

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

```javascript
var triangular = new Triangular( 2.0, 4.0, 3.0 );

var y = triangular.logpdf( 2.5 );
// returns ~-0.693
```

#### Triangular.prototype.pdf( x )

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

```javascript
var triangular = new Triangular( 2.0, 4.0, 3.0 );

var y = triangular.pdf( 2.5 );
// returns 0.5
```

#### Triangular.prototype.quantile( p )

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

```javascript
var triangular = new Triangular( 2.0, 4.0, 3.0 );

var y = triangular.quantile( 0.5 );
// returns 3.0

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

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* * *

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## Examples

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

var triangular = new Triangular( 2.0, 4.0, 3.0 );

var mu = triangular.mean;
// returns 3.0

var median = triangular.median;
// returns 3.0

var s2 = triangular.variance;
// returns ~0.167

var y = triangular.cdf( 2.5 );
// returns 0.125
```

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[triangular-distribution]: https://en.wikipedia.org/wiki/Triangular_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

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