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!

Variance

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

> [Lognormal][lognormal-distribution] distribution [variance][variance].

The [variance][variance] for a [lognormal][lognormal-distribution] random variable is

where μ is the location parameter and σ > 0 is the scale parameter. According to the definition, the _natural logarithm_ of a random variable from a
[lognormal distribution][lognormal-distribution] follows a [normal distribution][normal-distribution].

Installation

``bash npm install @stdlib/stats-base-dists-lognormal-variance`

`Usage`

`javascript var variance = require( '@stdlib/stats-base-dists-lognormal-variance' );`

#### variance( mu, sigma )

Returns the [variance][variance] for a [lognormal][lognormal-distribution] distribution with location mu and scale sigma.

`javascript var y = variance( 2.0, 1.0 ); // returns ~255.016

y = variance( 0.0, 1.0 ); // returns ~4.671

y = variance( -1.0, 2.0 ); // returns ~396.04`

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

`javascript var y = variance( NaN, 1.0 ); // returns NaN

y = variance( 0.0, NaN ); // returns NaN`

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

`javascript var y = variance( 0.0, 0.0 ); // returns NaN

y = variance( 0.0, -1.0 ); // returns NaN`

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var variance = require( '@stdlib/stats-base-dists-lognormal-variance' );

var opts = { 'dtype': 'float64' }; var mu = uniform( 10, -5.0, 5.0, opts ); var sigma = uniform( 10, 0.0, 20.0, opts );

logEachMap( 'µ: %0.4f, σ: %0.4f, Var(X;µ,σ): %0.4f', mu, sigma, variance );`

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/lognormal/variance.h"`

#### stdlib_base_dists_lognormal_variance( mu, sigma )

Returns the variance for a lognormal distribution with location mu and scale sigma.

`c double out = stdlib_base_dists_lognormal_variance( 0.0, 1.0 ); // returns ~4.671`

The function accepts the following arguments:

- mu: [in] doublelocation parameter. - sigma:[in] double scale parameter.

`c double stdlib_base_dists_lognormal_variance( const double mu, const double sigma );`

`$3`

`c #include "stdlib/stats/base/dists/lognormal/variance.h" #include #include

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 sigma; double mu; double y; int i;

for ( i = 0; i < 25; i++ ) { mu = random_uniform( -5.0, 5.0 ); sigma = random_uniform( 0.0, 20.0 ); y = stdlib_base_dists_lognormal_variance( mu, sigma ); printf( "µ: %lf, σ: %lf, Var(X;µ,σ): %lf\n", mu, sigma, 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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-lognormal-variance.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-lognormal-variance

[test-image]: https://github.com/stdlib-js/stats-base-dists-lognormal-variance/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/stats-base-dists-lognormal-variance/actions/workflows/test.yml?query=branch:v0.3.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-lognormal-variance/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-lognormal-variance?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

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

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-lognormal-variance/main/LICENSE

[lognormal-distribution]: https://en.wikipedia.org/wiki/Log-normal_distribution

[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution

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


  
    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!

`Variance`

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

> [Lognormal][lognormal-distribution] distribution [variance][variance].

The [variance][variance] for a [lognormal][lognormal-distribution] random variable is

where μ is the location parameter and σ > 0 is the scale parameter. According to the definition, the _natural logarithm_ of a random variable from a [lognormal distribution][lognormal-distribution] follows a [normal distribution][normal-distribution].

`Installation`

``bash npm install @stdlib/stats-base-dists-lognormal-variance `

`Usage`

`javascript var variance = require( '@stdlib/stats-base-dists-lognormal-variance' ); `

#### variance( mu, sigma )

Returns the [variance][variance] for a [lognormal][lognormal-distribution] distribution with location mu and scale sigma.

`javascript var y = variance( 2.0, 1.0 ); // returns ~255.016

y = variance( 0.0, 1.0 ); // returns ~4.671

y = variance( -1.0, 2.0 ); // returns ~396.04 `

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

`javascript var y = variance( NaN, 1.0 ); // returns NaN

y = variance( 0.0, NaN ); // returns NaN `

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

`javascript var y = variance( 0.0, 0.0 ); // returns NaN

y = variance( 0.0, -1.0 ); // returns NaN `

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var variance = require( '@stdlib/stats-base-dists-lognormal-variance' );

var opts = { 'dtype': 'float64' }; var mu = uniform( 10, -5.0, 5.0, opts ); var sigma = uniform( 10, 0.0, 20.0, opts );

logEachMap( 'µ: %0.4f, σ: %0.4f, Var(X;µ,σ): %0.4f', mu, sigma, variance ); `

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/lognormal/variance.h" `

#### stdlib_base_dists_lognormal_variance( mu, sigma )

Returns the variance for a lognormal distribution with location mu and scale sigma.

`c double out = stdlib_base_dists_lognormal_variance( 0.0, 1.0 ); // returns ~4.671 `

The function accepts the following arguments:

- mu: [in] double location parameter. - sigma: [in] double scale parameter.

`c double stdlib_base_dists_lognormal_variance( const double mu, const double sigma ); `

`$3`

`c #include "stdlib/stats/base/dists/lognormal/variance.h" #include #include

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 sigma; double mu; double y; int i;

for ( i = 0; i < 25; i++ ) { mu = random_uniform( -5.0, 5.0 ); sigma = random_uniform( 0.0, 20.0 ); y = stdlib_base_dists_lognormal_variance( mu, sigma ); printf( "µ: %lf, σ: %lf, Var(X;µ,σ): %lf\n", mu, sigma, y ); } } `

*

`Notice`

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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-lognormal-variance.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-lognormal-variance

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

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

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-lognormal-variance/main/LICENSE

[lognormal-distribution]: https://en.wikipedia.org/wiki/Log-normal_distribution

[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution

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