@stdlib/stats-base-dists-negative-binomial-ctor/README.md

Negative binomial distribution constructor.

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# Negative Binomial

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> Negative binomial distribution constructor.

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</section>

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<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-negative-binomial-ctor
```

</section>

<section class="usage">

## Usage

```javascript
var NegativeBinomial = require( '@stdlib/stats-base-dists-negative-binomial-ctor' );
```

#### NegativeBinomial( \[r, p] )

Returns a [negative binomial][negative-binomial-distribution] distribution object.

```javascript
var nbinomial = new NegativeBinomial();

var mu = nbinomial.mean;
// returns 1.0
```

By default, `r = 1.0` and `p = 0.5`. To create a distribution having a different `r` (number of trials until experiment is stopped) and `p` (success probability), provide the corresponding arguments.

```javascript
var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var mu = nbinomial.mean;
// returns 16.0
```

* * *

## nbinomial

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

### Writable Properties

#### nbinomial.r

Number of trials of the distribution. `r` **must** be a positive number.

```javascript
var nbinomial = new NegativeBinomial();

var r = nbinomial.r;
// returns 1.0

nbinomial.r = 4.5;

r = nbinomial.r;
// returns 4.5
```

#### nbinomial.p

Success probability of the distribution. `p` **must** be a number between 0 and 1.

```javascript
var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var p = nbinomial.p;
// returns 0.2

nbinomial.p = 0.7;

p = nbinomial.p;
// returns 0.7
```

* * *

### Computed Properties

#### NegativeBinomial.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var kurtosis = nbinomial.kurtosis;
// returns ~0.522
```

#### NegativeBinomial.prototype.mean

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

```javascript
var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var mu = nbinomial.mean;
// returns ~18.0
```

#### NegativeBinomial.prototype.mode

Returns the [mode][mode].

```javascript
var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var mode = nbinomial.mode;
// returns 16.0
```

#### NegativeBinomial.prototype.skewness

Returns the [skewness][skewness].

```javascript
var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var skewness = nbinomial.skewness;
// returns ~0.596
```

#### NegativeBinomial.prototype.stdev

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

```javascript
var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var s = nbinomial.stdev;
// returns ~6.708
```

#### NegativeBinomial.prototype.variance

Returns the [variance][variance].

```javascript
var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var s2 = nbinomial.variance;
// returns ~45.0
```

* * *

### Methods

#### NegativeBinomial.prototype.cdf( x )

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

```javascript
var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var y = nbinomial.cdf( 3.5 );
// returns ~0.033
```

#### NegativeBinomial.prototype.logpmf( x )

Evaluates the natural logarithm of the [probability mass function][pmf] (PMF).

```javascript
var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var y = nbinomial.logpmf( 4.0 );
// returns ~-3.775
```

#### NegativeBinomial.prototype.mgf( t )

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

```javascript
var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var y = nbinomial.mgf( 0.1 );
// returns ~1.66
```

#### NegativeBinomial.prototype.pmf( x )

Evaluates the [probability mass function][pmf] (PMF).

```javascript
var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var y = nbinomial.pmf( 4.0 );
// returns ~0.023
```

#### NegativeBinomial.prototype.quantile( p )

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

```javascript
var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var y = nbinomial.quantile( 0.5 );
// returns 15.0

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

</section>

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</section>

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* * *

<section class="examples">

## Examples

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

```javascript
var NegativeBinomial = require( '@stdlib/stats-base-dists-negative-binomial-ctor' );

var nbinomial = new NegativeBinomial( 10.0, 0.4 );

var mu = nbinomial.mean;
// returns 15.0

var mode = nbinomial.mode;
// returns 13.0

var s2 = nbinomial.variance;
// returns ~37.5

var y = nbinomial.cdf( 8.0 );
// returns ~0.135
```

</section>

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* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2024. The Stdlib [Authors][stdlib-authors].

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[negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function

[pmf]: https://en.wikipedia.org/wiki/Probability_mass_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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