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

Standard library statistical functions.

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# Fréchet

> Fréchet distribution constructor.

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## Usage

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

#### Frechet( \[alpha, s, m] )

Returns a [Fréchet][frechet-distribution] distribution object.

```javascript
var frechet = new Frechet();

var mu = frechet.mean;
// returns Infinity
```

By default, `alpha = 1.0`, `s = 1.0`, and `m = 0.0`. To create a distribution having a different `alpha` (shape), `s` (scale), and `m` (location), provide the corresponding arguments.

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.5 );

var mu = frechet.mean;
// returns ~10.59
```

* * *

## frechet

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

### Writable Properties

#### frechet.alpha

Shape parameter of the distribution. `alpha` **must** be a positive number.

```javascript
var frechet = new Frechet();

var alpha = frechet.alpha;
// returns 1.0

frechet.alpha = 0.5;

alpha = frechet.alpha;
// returns 0.5
```

#### frechet.s

Scale parameter of the distribution. `s` **must** be a positive number.

```javascript
var frechet = new Frechet( 2.0, 4.0, 1.5 );

var s = frechet.s;
// returns 4.0

frechet.s = 3.0;

s = frechet.s;
// returns 3.0
```

#### frechet.m

Location parameter of the distribution.

```javascript
var frechet = new Frechet( 2.0, 2.0, 4.0 );

var m = frechet.m;
// returns 4.0

frechet.m = 3.0;

m = frechet.m;
// returns 3.0
```

* * *

### Computed Properties

#### Frechet.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var entropy = frechet.entropy;
// returns ~2.82
```

#### Frechet.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var kurtosis = frechet.kurtosis;
// returns Infinity
```

#### Frechet.prototype.mean

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

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var mu = frechet.mean;
// returns ~16.705
```

#### Frechet.prototype.median

Returns the [median][median].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var median = frechet.median;
// returns ~15.151
```

#### Frechet.prototype.mode

Returns the [mode][mode].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var mode = frechet.mode;
// returns ~13.349
```

#### Frechet.prototype.skewness

Returns the [skewness][skewness].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var skewness = frechet.skewness;
// returns ~5.605
```

#### Frechet.prototype.stdev

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

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var s = frechet.stdev;
// returns ~6.245
```

#### Frechet.prototype.variance

Returns the [variance][variance].

```javascript
var frechet = new Frechet( 4.0, 12.0, 2.0 );

var s2 = frechet.variance;
// returns ~38.996
```

* * *

### Methods

#### Frechet.prototype.cdf( x )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.cdf( 2.5 );
// returns 0.0
```

#### Frechet.prototype.logcdf( x )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.logcdf( 2.5 );
// returns -Infinity
```

#### Frechet.prototype.logpdf( x )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.logpdf( 5.5 );
// returns ~-1.843
```

#### Frechet.prototype.pdf( x )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.pdf( 5.5 );
// returns ~0.158
```

#### Frechet.prototype.quantile( p )

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

```javascript
var frechet = new Frechet( 2.0, 4.0, 3.0 );

var y = frechet.quantile( 0.5 );
// returns ~7.804

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

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* * *

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## Examples

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

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

var frechet = new Frechet( 2.0, 4.0, 3.0 );

var mu = frechet.mean;
// returns ~10.09

var median = frechet.median;
// returns ~7.804

var s2 = frechet.variance;
// returns Infinity

var y = frechet.cdf( 2.5 );
// returns 0.0
```

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[frechet-distribution]: https://en.wikipedia.org/wiki/Fr%C3%A9chet_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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