npm package: @stdlib/stats-base-dists-pareto-type1-ctor
Description: Pareto (Type I) distribution constructor.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Pareto (Type I)

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> [Pareto (Type I)][pareto-distribution] distribution constructor.

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-pareto-type1-ctor
```

</section>

<section class="usage">

## Usage

```javascript
var Pareto1 = require( '@stdlib/stats-base-dists-pareto-type1-ctor' );
```

#### Pareto1( \[alpha, beta] )

Returns a [Pareto (Type I)][pareto-distribution] distribution object.

```javascript
var pareto1 = new Pareto1();

var mu = pareto1.mean;
// returns Infinity
```

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

```javascript
var pareto1 = new Pareto1( 2.0, 4.0 );

var mu = pareto1.mean;
// returns 8.0
```

* * *

## pareto1

A [Pareto (Type I)][pareto-distribution] distribution object has the following properties and methods...

### Writable Properties

#### pareto1.alpha

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

```javascript
var pareto1 = new Pareto1();

var alpha = pareto1.alpha;
// returns 1.0

pareto1.alpha = 3.0;

alpha = pareto1.alpha;
// returns 3.0
```

#### pareto1.beta

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

```javascript
var pareto1 = new Pareto1( 2.0, 4.0 );

var beta = pareto1.beta;
// returns 4.0

pareto1.beta = 3.0;

beta = pareto1.beta;
// returns 3.0
```

* * *

### Computed Properties

#### Pareto1.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var pareto1 = new Pareto1( 4.0, 12.0 );

var entropy = pareto1.entropy;
// returns ~2.349
```

#### Pareto1.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var pareto1 = new Pareto1( 6.0, 12.0 );

var kurtosis = pareto1.kurtosis;
// returns ~35.667
```

#### Pareto1.prototype.mean

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

```javascript
var pareto1 = new Pareto1( 4.0, 12.0 );

var mu = pareto1.mean;
// returns 16.0
```

#### Pareto1.prototype.median

Returns the [median][median].

```javascript
var pareto1 = new Pareto1( 4.0, 12.0 );

var median = pareto1.median;
// returns ~14.27
```

#### Pareto1.prototype.mode

Returns the [mode][mode].

```javascript
var pareto1 = new Pareto1( 4.0, 12.0 );

var mode = pareto1.mode;
// returns 12.0
```

#### Pareto1.prototype.skewness

Returns the [skewness][skewness].

```javascript
var pareto1 = new Pareto1( 4.0, 12.0 );

var skewness = pareto1.skewness;
// returns ~7.071
```

#### Pareto1.prototype.variance

Returns the [variance][variance].

```javascript
var pareto1 = new Pareto1( 4.0, 12.0 );

var s2 = pareto1.variance;
// returns 32.0
```

* * *

### Methods

#### Pareto1.prototype.cdf( x )

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

```javascript
var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.cdf( 3.5 );
// returns 0.0
```

#### Pareto1.prototype.logcdf( x )

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

```javascript
var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.logcdf( 3.5 );
// returns -Infinity
```

#### Pareto1.prototype.logpdf( x )

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

```javascript
var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.logpdf( 5.0 );
// returns ~-1.363
```

#### Pareto1.prototype.pdf( x )

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

```javascript
var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.pdf( 5.0 );
// returns ~0.256
```

#### Pareto1.prototype.quantile( p )

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

```javascript
var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.quantile( 0.5 );
// returns ~5.657

y = pareto1.quantile( 1.9 );
// returns NaN
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

```javascript
var Pareto1 = require( '@stdlib/stats-base-dists-pareto-type1-ctor' );

var pareto1 = new Pareto1( 2.0, 4.0 );

var mu = pareto1.mean;
// returns 8.0

var median = pareto1.median;
// returns ~5.657

var s2 = pareto1.variance;
// returns Infinity

var y = pareto1.cdf( 2.0 );
// returns 0.0
```

</section>

<!-- /.examples -->

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</section>

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</section>

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<section class="main-repo" >

* * *

## 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].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-pareto-type1-ctor/main/LICENSE

[pareto-distribution]: https://en.wikipedia.org/wiki/Pareto_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

[variance]: https://en.wikipedia.org/wiki/Variance

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