# @stdlib/stats-base-dists-weibull-variance

0.2.2 • Public • Published

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# Variance

Weibull distribution variance.

The variance for a Weibull random variable is

where `λ > 0` is the shape parameter, `k > 0` is the scale parameter, and `Γ` denotes the gamma function.

## Installation

`npm install @stdlib/stats-base-dists-weibull-variance`

## Usage

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

#### variance( k, lambda )

Returns the variance of a Weibull distribution with parameters `k` (shape parameter) and `lambda` (scale parameter).

```var v = variance( 1.0, 1.0 );
// returns 1.0

v = variance( 4.0, 12.0 );
// returns ~9.311

v = variance( 8.0, 2.0 );
// returns ~0.078```

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

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

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

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

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

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

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

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

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

## Examples

```var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var variance = require( '@stdlib/stats-base-dists-weibull-variance' );

var lambda;
var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
k = ( randu()*10.0 ) + EPS;
lambda = ( randu()*10.0 ) + EPS;
v = variance( k, lambda );
console.log( 'k: %d, λ: %d, Var(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}```

## Notice

This package is part of 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, see the main project repository.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-weibull-variance`

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