npm package: @stdlib/stats-base-dists-pareto-type1-stdev
Description: Pareto (Type I) distribution standard deviation.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Standard Deviation

[![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 [standard deviation][standard-deviation].

<!-- 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 [standard deviation][standard-deviation] for a [Pareto (Type I)][pareto-distribution] random variable is

<!-- <equation class="equation" label="eq:pareto_type1_stdev" align="center" raw="\operatorname{SD}\left( X \right) = \begin{cases} \infty & \text{for }\alpha\in(0,2] \\ \sqrt{ \frac{\beta^2\alpha}{(\alpha-1)^2(\alpha-2)} } & \text{for }\alpha>2 \end{cases}" alt="Standard deviation for a Pareto (Type I) distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{SD}\left( X \right) = \begin{cases} \infty &amp; \text{for }\alpha\in(0,2] \\ \sqrt{ \frac{\beta^2\alpha}{(\alpha-1)^2(\alpha-2)} } &amp; \text{for }\alpha&gt;2 \end{cases}" data-equation="eq:pareto_type1_stdev">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@e1fbdee688c5409e4cc6b0cd06d90b1cd2abd67c/lib/node_modules/@stdlib/stats/base/dists/pareto-type1/stdev/docs/img/equation_pareto_type1_stdev.svg" alt="Standard deviation 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-stdev
```

</section>

<section class="usage">

## Usage

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

#### stdev( alpha, beta )

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

```javascript
var v = stdev( 2.5, 1.0 );
// returns ~1.491

v = stdev( 4.0, 12.0 );
// returns ~5.657

v = stdev( 8.0, 2.0 );
// returns ~0.33
```

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

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

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

If provided `0 < alpha <= 2`, the function returns `+Infinity`.

```javascript
var v = stdev( 0.5, 2.0 );
// returns Infinity

v = stdev( 1.5, 1.0 );
// returns Infinity
```

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

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

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

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

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

v = stdev( 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 stdev = require( '@stdlib/stats-base-dists-pareto-type1-stdev' );

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, SD(X;α,β): %0.4f', alpha, beta, stdev );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- 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 -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/base/dists/pareto-type1/stdev.h"
```

#### stdlib_base_dists_pareto_type1_stdev( alpha, beta )

Returns the standard deviation of a Pareto (Type I) distribution.

```c
double out = stdlib_base_dists_pareto_type1_stdev( 2.5, 1.0 );
// returns ~1.491
```

The function accepts the following arguments:

-   **alpha**: `[in] double` first shape parameter.
-   **beta**: `[in] double` second shape parameter.

```c
double stdlib_base_dists_pareto_type1_stdev( const double alpha, const double beta );
```

</section>

<!-- /.usage -->

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<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/pareto-type1/stdev.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double alpha;
    double beta;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        alpha = random_uniform( 0.0, 10.0 );
        beta = random_uniform( 0.0, 10.0 );
        y = stdlib_base_dists_pareto_type1_stdev( alpha, beta );
        printf( "α: %lf, β: %lf, SD(X;α,β): %lf\n", alpha, beta, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="references">

</section>

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<section class="related">

</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; 2016-2026. The Stdlib [Authors][stdlib-authors].

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

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