About stdlib…

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we’ve built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Standard Deviation

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

[F][f-distribution] distribution [standard deviation][standard-deviation].

The [standard deviation][standard-deviation] for a [F][f-distribution] random variable is

math
\sigma = \sqrt{2} \tfrac{d_1}{d_2-2} \sqrt{\tfrac{d_1+d_2-2}{d_1 \cdot (d_2-4)}}

for d1 > 0 and d2 > 4. Otherwise, the standard deviation is not defined.

## Installation

bash
npm install @stdlib/stats-base-dists-f-stdev

Alternatively,

- To load the package in a website via a script tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [deno][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [umd][umd-url] branch (see [README][umd-readme]).

The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage

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

#### stdev( d1, d2 )

Returns the [standard deviation][standard-deviation] of an [F][f-distribution] distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

javascript
var v = stdev( 4.0, 5.0 );
// returns ~3.118

v = stdev( 4.0, 12.0 );
// returns ~1.122

v = stdev( 8.0, 5.0 );
// returns ~2.764

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

javascript
var v = stdev( NaN, 5.0 );
// returns NaN

v = stdev( 3.0, NaN );
// returns NaN

If provided d1 <= 0, the function returns NaN.

javascript
var v = stdev( 0.0, 5.0 );
// returns NaN

v = stdev( -1.0, 5.0 );
// returns NaN

If provided d2 <= 4, the function returns NaN.

javascript
var v = stdev( 3.0, 4.0 );
// returns NaN

v = stdev( 3.0, -1.0 );
// returns NaN

## Examples

javascript
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var stdev = require( '@stdlib/stats-base-dists-f-stdev' );

var d1;
var d2;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    d1 = ( randu()*10.0 ) + EPS;
    d2 = ( randu()*20.0 ) + EPS;
    v = stdev( d1, d2 );
    console.log( 'd1: %d, d2: %d, SD(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) );
}

## C APIs

### Usage

c
#include "stdlib/stats/base/dists/f/stdev.h"

#### stdlib_base_dists_f_stdev( d1, d2 )

Evaluates the [standard deviation][standard-deviation] of an [F][f-distribution] distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

c
double out = stdlib_base_dists_f_stdev( 3.0, 5.0 );
// returns ~3.333

The function accepts the following arguments:

- d1: [in] double numerator degrees of freedom.
- d2: [in] double denominator degrees of freedom.

c
double stdlib_base_dists_f_stdev( const double d1, const double d2 );

### Examples

c
#include "stdlib/stats/base/dists/f/stdev.h"
#include "stdlib/constants/float64/eps.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 d1;
    double d2;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        d1 = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        d2 = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
        y = stdlib_base_dists_f_stdev( d1, d2 );
        printf( "d1: %lf, d2: %lf, SD(X;d1,d2): %lf\n", d1, d2, y );
    }
}

*

## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].