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https://github.com/stdlib-js/random-base-normal

Normally distributed pseudorandom numbers.
https://github.com/stdlib-js/random-base-normal

gaussian generator javascript math mathematics node node-js nodejs normal prng pseudorandom rand randn random rng seed seedable statistics stats stdlib

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Normally distributed pseudorandom numbers.

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README 

        



  

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# Normal Random Numbers



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



> [Normally][normal] distributed pseudorandom numbers.



## Installation



```bash

npm install @stdlib/random-base-normal

```



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 normal = require( '@stdlib/random-base-normal' );

```



#### normal( mu, sigma )



Returns a pseudorandom number drawn from a [normal][normal] distribution with parameters `mu` (mean) and `sigma` (standard deviation).



```javascript

var r = normal( 2.0, 5.0 );

// returns 

```



If `mu` or `sigma` is `NaN` or `sigma <= 0`, the function returns `NaN`.



```javascript

var r = normal( 2.0, -2.0 );

// returns NaN



r = normal( NaN, 5.0 );

// returns NaN



r = normal( 2.0, NaN );

// returns NaN

```



#### normal.factory( \[mu, sigma, ]\[options] )



Returns a pseudorandom number generator (PRNG) for generating pseudorandom numbers drawn from a [normal][normal] distribution.



```javascript

var rand = normal.factory();



var r = rand( 0.1, 1.5 );

// returns 

```



If provided `mu` and `sigma`, the returned generator returns random variates from the specified distribution.



```javascript

// Draw from normal( 10.0, 2.0 ) distribution:

var rand = normal.factory( 10.0, 2.0 );



var r = rand();

// returns 



r = rand();

// returns 

```



If not provided `mu` and `sigma`, the returned generator requires that both parameters be provided at each invocation.



```javascript

var rand = normal.factory();



var r = rand( 0.0, 1.0 );

// returns 



r = rand( -2.0, 2.0 );

// returns 

```



The function accepts the following `options`:



-   **prng**: pseudorandom number generator for generating uniformly distributed pseudorandom numbers on the interval `[0,1)`. If provided, the function **ignores** both the `state` and `seed` options. In order to seed the returned pseudorandom number generator, one must seed the provided `prng` (assuming the provided `prng` is seedable).

-   **seed**: pseudorandom number generator seed.

-   **state**: a [`Uint32Array`][@stdlib/array/uint32] containing pseudorandom number generator state. If provided, the function ignores the `seed` option.

-   **copy**: `boolean` indicating whether to copy a provided pseudorandom number generator state. Setting this option to `false` allows sharing state between two or more pseudorandom number generators. Setting this option to `true` ensures that a returned generator has exclusive control over its internal state. Default: `true`.



To use a custom PRNG as the underlying source of uniformly distributed pseudorandom numbers, set the `prng` option.



```javascript

var minstd = require( '@stdlib/random-base-minstd' );



var rand = normal.factory({

    'prng': minstd.normalized

});



var r = rand( 1.0, 2.0 );

// returns 

```



To seed a pseudorandom number generator, set the `seed` option.



```javascript

var rand1 = normal.factory({

    'seed': 12345

});



var r1 = rand1( 1.0, 2.0 );

// returns 



var rand2 = normal.factory( 1.0, 2.0, {

    'seed': 12345

});



var r2 = rand2();

// returns 



var bool = ( r1 === r2 );

// returns true

```



To return a generator having a specific initial state, set the generator `state` option.



```javascript

var rand;

var bool;

var r;

var i;



// Generate pseudorandom numbers, thus progressing the generator state:

for ( i = 0; i < 1000; i++ ) {

    r = normal( 1.0, 2.0 );

}



// Create a new PRNG initialized to the current state of `normal`:

rand = normal.factory({

    'state': normal.state

});



// Test that the generated pseudorandom numbers are the same:

bool = ( rand( 1.0, 2.0 ) === normal( 1.0, 2.0 ) );

// returns true

```



#### normal.NAME



The generator name.



```javascript

var str = normal.NAME;

// returns 'normal'

```



#### normal.PRNG



The underlying pseudorandom number generator.



```javascript

var prng = normal.PRNG;

// returns 

```



#### normal.seed



The value used to seed `normal()`.



```javascript

var rand;

var r;

var i;



// Generate pseudorandom values...

for ( i = 0; i < 100; i++ ) {

    r = normal( 2.0, 2.0 );

}



// Generate the same pseudorandom values...

rand = normal.factory( 2.0, 2.0, {

    'seed': normal.seed

});

for ( i = 0; i < 100; i++ ) {

    r = rand();

}

```



If provided a PRNG for uniformly distributed numbers, this value is `null`.



```javascript

var rand = normal.factory({

    'prng': Math.random

});



var seed = rand.seed;

// returns null

```



#### normal.seedLength



Length of generator seed.



```javascript

var len = normal.seedLength;

// returns 

```



If provided a PRNG for uniformly distributed numbers, this value is `null`.



```javascript

var rand = normal.factory({

    'prng': Math.random

});



var len = rand.seedLength;

// returns null

```



#### normal.state



Writable property for getting and setting the generator state.



```javascript

var r = normal( 2.0, 5.0 );

// returns 



r = normal( 2.0, 5.0 );

// returns 



// ...



// Get a copy of the current state:

var state = normal.state;

// returns 



r = normal( 2.0, 5.0 );

// returns 



r = normal( 2.0, 5.0 );

// returns 



// Reset the state:

normal.state = state;



// Replay the last two pseudorandom numbers:

r = normal( 2.0, 5.0 );

// returns 



r = normal( 2.0, 5.0 );

// returns 



// ...

```



If provided a PRNG for uniformly distributed numbers, this value is `null`.



```javascript

var rand = normal.factory({

    'prng': Math.random

});



var state = rand.state;

// returns null

```



#### normal.stateLength



Length of generator state.



```javascript

var len = normal.stateLength;

// returns 

```



If provided a PRNG for uniformly distributed numbers, this value is `null`.



```javascript

var rand = normal.factory({

    'prng': Math.random

});



var len = rand.stateLength;

// returns null

```



#### normal.byteLength



Size of generator state.



```javascript

var sz = normal.byteLength;

// returns 

```



If provided a PRNG for uniformly distributed numbers, this value is `null`.



```javascript

var rand = normal.factory({

    'prng': Math.random

});



var sz = rand.byteLength;

// returns null

```



#### normal.toJSON()



Serializes the pseudorandom number generator as a JSON object.



```javascript

var o = normal.toJSON();

// returns { 'type': 'PRNG', 'name': '...', 'state': {...}, 'params': [] }

```



If provided a PRNG for uniformly distributed numbers, this method returns `null`.



```javascript

var rand = normal.factory({

    'prng': Math.random

});



var o = rand.toJSON();

// returns null

```



## Notes



-   If PRNG state is "shared" (meaning a state array was provided during PRNG creation and **not** copied) and one sets the generator state to a state array having a different length, the PRNG does **not** update the existing shared state and, instead, points to the newly provided state array. In order to synchronize PRNG output according to the new shared state array, the state array for **each** relevant PRNG must be **explicitly** set.

-   If PRNG state is "shared" and one sets the generator state to a state array of the same length, the PRNG state is updated (along with the state of all other PRNGs sharing the PRNG's state array).



## Examples



```javascript

var normal = require( '@stdlib/random-base-normal' );



var seed;

var rand;

var i;



// Generate pseudorandom numbers...

for ( i = 0; i < 100; i++ ) {

    console.log( normal( 0.0, 1.0 ) );

}



// Create a new pseudorandom number generator...

seed = 1234;

rand = normal.factory( 5.0, 2.0, {

    'seed': seed

});

for ( i = 0; i < 100; i++ ) {

    console.log( rand() );

}



// Create another pseudorandom number generator using a previous seed...

rand = normal.factory( 0.0, 1.0, {

    'seed': normal.seed

});

for ( i = 0; i < 100; i++ ) {

    console.log( rand() );

}

```



* * *



## See Also



-   [`@stdlib/random-array/normal`][@stdlib/random/array/normal]: create an array containing pseudorandom numbers drawn from a normal distribution.

-   [`@stdlib/random-iter/normal`][@stdlib/random/iter/normal]: create an iterator for generating pseudorandom numbers drawn from a normal distribution.

-   [`@stdlib/random-streams/normal`][@stdlib/random/streams/normal]: create a readable stream for generating pseudorandom numbers drawn from a normal distribution.



* * *



## 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 © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/random-base-normal.svg

[npm-url]: https://npmjs.org/package/@stdlib/random-base-normal



[test-image]: https://github.com/stdlib-js/random-base-normal/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/random-base-normal/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/random-base-normal/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/random-base-normal?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[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/random-base-normal/tree/deno

[deno-readme]: https://github.com/stdlib-js/random-base-normal/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/random-base-normal/tree/umd

[umd-readme]: https://github.com/stdlib-js/random-base-normal/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/random-base-normal/tree/esm

[esm-readme]: https://github.com/stdlib-js/random-base-normal/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/random-base-normal/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/random-base-normal/main/LICENSE



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



[@stdlib/array/uint32]: https://github.com/stdlib-js/array-uint32



[@stdlib/random/array/normal]: https://github.com/stdlib-js/random-array-normal



[@stdlib/random/iter/normal]: https://github.com/stdlib-js/random-iter-normal



[@stdlib/random/streams/normal]: https://github.com/stdlib-js/random-streams-normal