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237 changes: 237 additions & 0 deletions lib/node_modules/@stdlib/stats/base/dists/anglit/stdev/README.md
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<!--

@license Apache-2.0

Copyright (c) 2026 The Stdlib Authors.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

-->

# Standard Deviation

> [Anglit][anglit-distribution] distribution [standard deviation][stdev].

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

The [standard deviation][stdev] for an [anglit][anglit-distribution] random variable with location parameter `mu` and scale parameter `sigma` is

<!-- <equation class="equation" label="eq:anglit_stdev" align="center" raw="\operatorname{SD}(X) = \sigma \sqrt{\left({\frac{\pi^{2}}{16}}-\frac{1}{2}\right)}" alt="Standard deviation for an anglit distribution."> -->
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While previewing the markdown documentation the equation is not generated here properly. Mind fixing that as well.
Re:-

Image


```math
\operatorname{SD}(X) = \sigma \sqrt{\left({\frac{\pi^{2}}{16}}-\frac{1}{2}\right)}
```

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="usage">

## Usage

```javascript
var stdev = require( '@stdlib/stats/base/dists/anglit/stdev' );
```

#### stdev( mu, sigma )

Returns the [standard deviation][stdev] for an [anglit][anglit-distribution] distribution with location parameter `mu` and scale parameter `sigma`.

```javascript
var y = stdev( 0.0, 1.0 );
// returns ~0.342

y = stdev( 2.0, 4.0 );
// returns ~1.367
```

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

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

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

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

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

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

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

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

var opts = {
'dtype': 'float64'
};
var mu = uniform( 10, -50.0, 50.0, opts );
var sigma = uniform( 10, 0.1, 20.0, opts );

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

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

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

#### stdlib_base_dists_anglit_stdev( mu, sigma )

Returns the [standard deviation][stdev] for an [anglit][anglit-distribution] distribution with location parameter `mu` and scale parameter `sigma`.

```c
double out = stdlib_base_dists_anglit_stdev( 0.0, 1.0 );
// returns ~0.342
```

The function accepts the following arguments:

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

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

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/anglit/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 sigma;
double mu;
double y;
int i;

for ( i = 0; i < 10; i++ ) {
mu = random_uniform( -50.0, 50.0 );
sigma = random_uniform( 0.1, 20.0 );
y = stdlib_base_dists_anglit_stdev( mu, sigma );
printf( "µ: %lf, σ: %lf, SD(X;µ,σ): %lf\n", mu, sigma, y );
}
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->


<section class="related">

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[anglit-distribution]: https://en.wikipedia.org/wiki/Anglit_distribution

[stdev]: https://en.wikipedia.org/wiki/Standard_deviation

</section>

<!-- /.links -->
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/**
* @license Apache-2.0
*
* Copyright (c) 2026 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

'use strict';

// MODULES //

var bench = require( '@stdlib/bench' );
var uniform = require( '@stdlib/random/array/uniform' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var pkg = require( './../package.json' ).name;
var stdev = require( './../lib' );


// MAIN //

bench( pkg, function benchmark( b ) {
var sigma;
var opts;
var mu;
var y;
var i;

opts = {
'dtype': 'float64'
};
mu = uniform( 100, -50.0, 50.0, opts );
sigma = uniform( 100, 0.1, 20.0, opts );

b.tic();
for ( i = 0; i < b.iterations; i++ ) {
y = stdev( mu[ i % mu.length ], sigma[ i % sigma.length ] );
if ( isnan( y ) ) {
b.fail( 'should not return NaN' );
}
}
b.toc();
if ( isnan( y ) ) {
b.fail( 'should not return NaN' );
}
b.pass( 'benchmark finished' );
b.end();
});
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/**
* @license Apache-2.0
*
* Copyright (c) 2026 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

'use strict';

// MODULES //

var resolve = require( 'path' ).resolve;
var bench = require( '@stdlib/bench' );
var uniform = require( '@stdlib/random/array/uniform' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var tryRequire = require( '@stdlib/utils/try-require' );
var format = require( '@stdlib/string/format' );
var pkg = require( './../package.json' ).name;


// VARIABLES //

var stdev = tryRequire( resolve( __dirname, './../lib/native.js' ) );
var opts = {
'skip': ( stdev instanceof Error )
};


// MAIN //

bench( format( '%s::native', pkg ), opts, function benchmark( b ) {
var sigma;
var opts;
var mu;
var y;
var i;

opts = {
'dtype': 'float64'
};
mu = uniform( 100, -50.0, 50.0, opts );
sigma = uniform( 100, 0.1, 20.0, opts );

b.tic();
for ( i = 0; i < b.iterations; i++ ) {
y = stdev( mu[ i % mu.length ], sigma[ i % sigma.length ] );
if ( isnan( y ) ) {
b.fail( 'should not return NaN' );
}
}
b.toc();
if ( isnan( y ) ) {
b.fail( 'should not return NaN' );
}
b.pass( 'benchmark finished' );
b.end();
});
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