npm package: @stdlib/stats-base-dists-pareto-type1-median
Description: Pareto (Type I) distribution median.
Author: The Stdlib Authors
Latest version: 0.1.3

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  <summary>
    About stdlib...
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# Median

[![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 [median][median].

<!-- 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">

The [median][median] for a [Pareto (Type I)][pareto-distribution] random variable is

<!-- <equation class="equation" label="eq:pareto_type1_median" align="center" raw="\operatorname{Median}\left( X \right) = \beta \sqrt[\alpha]{2}" alt="Median for a Pareto (Type I) distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Median}\left( X \right) = \beta \sqrt[\alpha]{2}" data-equation="eq:pareto_type1_median">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/pareto-type1/median/docs/img/equation_pareto_type1_median.svg" alt="Median for a Pareto (Type I) distribution.">
    <br>
</div>

<!-- </equation> -->

where `α > 0` is the shape parameter and `β > 0` is the scale parameter.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### median( alpha, beta )

Returns the [median][median] of a [Pareto (Type I)][pareto-distribution] distribution with parameters `alpha` (shape parameter) and `beta` (scale parameter).

```javascript
var v = median( 2.0, 1.0 );
// returns ~1.414

v = median( 4.0, 12.0 );
// returns ~14.27

v = median( 8.0, 2.0 );
// returns ~2.181
```

If provided `NaN` as any argument, the function returns `NaN`.

```javascript
var v = median( NaN, 2.0 );
// returns NaN

v = median( 2.0, NaN );
// returns NaN
```

If provided `alpha <= 0`, the function returns `NaN`.

```javascript
var v = median( 0.0, 1.0 );
// returns NaN

v = median( -1.0, 1.0 );
// returns NaN
```

If provided `beta <= 0`, the function returns `NaN`.

```javascript
var v = median( 1.0, 0.0 );
// returns NaN

v = median( 1.0, -1.0 );
// 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 uniform = require( '@stdlib/random-array-uniform' );
var EPS = require( '@stdlib/constants-float64-eps' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var median = require( '@stdlib/stats-base-dists-pareto-type1-median' );

var opts = {
    'dtype': 'float64'
};
var alpha = uniform( 10, EPS, 10.0, opts );
var beta = uniform( 10, EPS, 10.0, opts );

logEachMap( 'α: %0.4f, β: %0.4f, Median(X;α,β): %0.4f', alpha, beta, median );
```

</section>

<!-- /.examples -->

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<section class="references">

</section>

<!-- /.references -->

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<section class="related">

</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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[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-pareto-type1-median?branch=main

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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/stats-base-dists-pareto-type1-median/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-pareto-type1-median/blob/deno/README.md
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[esm-url]: https://github.com/stdlib-js/stats-base-dists-pareto-type1-median/tree/esm
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[branches-url]: https://github.com/stdlib-js/stats-base-dists-pareto-type1-median/blob/main/branches.md

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

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

[median]: https://en.wikipedia.org/wiki/Median

</section>

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