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# Inverse Gamma

> Inverse gamma distribution constructor.

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</section>

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## Usage

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

#### InvGamma( \[alpha, beta] )

Returns an [inverse gamma][invgamma-distribution] distribution object.

```javascript
var invgamma = new InvGamma();

var mode = invgamma.mode;
// returns 0.5
```

By default, `alpha = 1.0` and `beta = 1.0`. To create a distribution having a different `alpha` (shape parameter) and `beta` (rate parameter), provide the corresponding arguments.

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

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

* * *

## invgamma

An [inverse gamma][invgamma-distribution] distribution object has the following properties and methods...

### Writable Properties

#### invgamma.alpha

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

```javascript
var invgamma = new InvGamma();

var alpha = invgamma.alpha;
// returns 1.0

invgamma.alpha = 3.0;

alpha = invgamma.alpha;
// returns 3.0
```

#### invgamma.beta

Rate parameter of the distribution. `beta` **must** be a positive number.

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var b = invgamma.beta;
// returns 4.0

invgamma.beta = 3.0;

b = invgamma.beta;
// returns 3.0
```

* * *

### Computed Properties

#### InvGamma.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var invgamma = new InvGamma( 6.0, 12.0 );

var kurtosis = invgamma.kurtosis;
// returns 19.0
```

#### InvGamma.prototype.mean

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

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

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

#### InvGamma.prototype.mode

Returns the [mode][mode].

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

var mode = invgamma.mode;
// returns 2.4
```

#### InvGamma.prototype.skewness

Returns the [skewness][skewness].

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

var skewness = invgamma.skewness;
// returns ~5.657
```

#### InvGamma.prototype.stdev

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

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

var s = invgamma.stdev;
// returns ~2.828
```

#### InvGamma.prototype.variance

Returns the [variance][variance].

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

var s2 = invgamma.variance;
// returns 8.0
```

* * *

### Methods

#### InvGamma.prototype.cdf( x )

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

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.cdf( 0.5 );
// returns ~0.003
```

#### InvGamma.prototype.logpdf( x )

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

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.logpdf( 0.8 );
// returns ~-1.558
```

#### InvGamma.prototype.pdf( x )

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

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.pdf( 0.8 );
// returns ~0.211
```

#### InvGamma.prototype.quantile( p )

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

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.quantile( 0.5 );
// returns ~2.383

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

</section>

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* * *

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## Examples

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

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

var invgamma = new InvGamma( 3.0, 4.0 );

var mu = invgamma.mean;
// returns 2.0

var mode = invgamma.mode;
// returns 1.0

var s2 = invgamma.variance;
// returns 4.0

var y = invgamma.cdf( 0.8 );
// returns ~0.125
```

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[invgamma-distribution]: https://en.wikipedia.org/wiki/Inverse_Gamma_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

[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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