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Standard Deviation

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

[Exponential][exponential-distribution] distribution [standard deviation][standard-deviation].

The [standard deviation][standard-deviation] for an [exponential][exponential-distribution] random variable is

math
\sigma = \lambda^{-1}

where λ is the rate parameter.

## Installation

bash
npm install @stdlib/stats-base-dists-exponential-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-exponential-stdev' );

#### stdev( lambda )

Returns the [standard deviation][standard-deviation] of a [exponential][exponential-distribution] distribution with rate parameter lambda.

javascript
var v = stdev( 9.0 );
// returns ~0.11

v = stdev( 0.5 );
// returns 2.0

If provided lambda < 0, the function returns NaN.

javascript
var v = stdev( -1.0 );
// returns NaN

## Examples

javascript
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var stdev = require( '@stdlib/stats-base-dists-exponential-stdev' );

var lambda;
var v;
var i;

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

## C APIs

### Usage

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

#### stdlib_base_dists_exponential_stdev( lambda )

Returns the standard deviation of an exponential distribution.

c
double out = stdlib_base_dists_exponential_stdev( 9.0 );
// returns ~0.111

The function accepts the following arguments:

- lambda: [in] double rate parameter.

c
double stdlib_base_dists_exponential_stdev( const double lambda );

### Examples

c
#include "stdlib/stats/base/dists/exponential/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 lambda;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        lambda = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_exponential_stdev( lambda );
        printf( "λ: %lf, SD(X;λ): %lf\n", lambda, 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].