npm package: @stdlib/stats-base-dists-cosine-ctor
Description: Raised cosine distribution constructor.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Cosine

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

> Raised cosine distribution constructor.

<!-- 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 -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-cosine-ctor
```

</section>

<section class="usage">

## Usage

```javascript
var Cosine = require( '@stdlib/stats-base-dists-cosine-ctor' );
```

#### Cosine( \[mu, s] )

Returns a [raised cosine][cosine-distribution] distribution object.

```javascript
var cosine = new Cosine();

var mu = cosine.mean;
// returns 0.0
```

By default, `mu = 0.0` and `s = 1.0`. To create a distribution having a different `mu` (location parameter) and `s` (scale parameter), provide the corresponding arguments.

```javascript
var cosine = new Cosine( 2.0, 4.0 );

var mu = cosine.mean;
// returns 2.0
```

* * *

## cosine

A [raised cosine][cosine-distribution] distribution object has the following properties and methods...

### Writable Properties

#### cosine.mu

Location parameter of the distribution.

```javascript
var cosine = new Cosine();

var mu = cosine.mu;
// returns 0.0

cosine.mu = 3.0;

mu = cosine.mu;
// returns 3.0
```

#### cosine.s

Scale parameter of the distribution. `s` **must** be a positive number.

```javascript
var cosine = new Cosine( 2.0, 4.0 );

var s = cosine.s;
// returns 4.0

cosine.s = 3.0;

s = cosine.s;
// returns 3.0
```

* * *

### Computed Properties

#### Cosine.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var cosine = new Cosine( 4.0, 12.0 );

var kurtosis = cosine.kurtosis;
// returns ~-0.594
```

#### Cosine.prototype.mean

Returns the [expected value][expected-value].

```javascript
var cosine = new Cosine( 4.0, 12.0 );

var mu = cosine.mean;
// returns 4.0
```

#### Cosine.prototype.median

Returns the [median][median].

```javascript
var cosine = new Cosine( 4.0, 12.0 );

var median = cosine.median;
// returns 4.0
```

#### Cosine.prototype.mode

Returns the [mode][mode].

```javascript
var cosine = new Cosine( 4.0, 12.0 );

var mode = cosine.mode;
// returns 4.0
```

#### Cosine.prototype.skewness

Returns the [skewness][skewness].

```javascript
var cosine = new Cosine( 4.0, 12.0 );

var skewness = cosine.skewness;
// returns 0.0
```

#### Cosine.prototype.stdev

Returns the [standard deviation][standard-deviation].

```javascript
var cosine = new Cosine( 4.0, 12.0 );

var s = cosine.stdev;
// returns ~4.338
```

#### Cosine.prototype.variance

Returns the [variance][variance].

```javascript
var cosine = new Cosine( 4.0, 12.0 );

var s2 = cosine.variance;
// returns ~18.819
```

* * *

### Methods

#### Cosine.prototype.cdf( x )

Evaluates the [cumulative distribution function][cdf] (CDF).

```javascript
var cosine = new Cosine( 2.0, 4.0 );

var y = cosine.cdf( 0.5 );
// returns ~0.165
```

#### Cosine.prototype.logcdf( x )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).

```javascript
var cosine = new Cosine( 2.0, 4.0 );

var y = cosine.logcdf( 0.5 );
// returns ~-1.799
```

#### Cosine.prototype.logpdf( x )

Evaluates the natural logarithm of the [probability density function][pdf] (PDF).

```javascript
var cosine = new Cosine( 2.0, 4.0 );

var y = cosine.logpdf( 0.8 );
// returns ~-1.617
```

#### Cosine.prototype.mgf( t )

Evaluates the [moment-generating function][mgf] (MGF).

```javascript
var cosine = new Cosine( 2.0, 4.0 );

var y = cosine.mgf( 0.2 );
// returns ~1.555
```

#### Cosine.prototype.pdf( x )

Evaluates the [probability density function][pdf] (PDF).

```javascript
var cosine = new Cosine( 2.0, 4.0 );

var y = cosine.pdf( 2.0 );
// returns 0.25
```

#### Cosine.prototype.quantile( p )

Evaluates the [quantile function][quantile-function] at probability `p`.

```javascript
var cosine = new Cosine( 2.0, 4.0 );

var y = cosine.quantile( 0.9 );
// returns ~3.929

y = cosine.quantile( 1.9 );
// 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 Cosine = require( '@stdlib/stats-base-dists-cosine-ctor' );

var cosine = new Cosine( 2.0, 4.0 );

var mean = cosine.mean;
// returns 2.0

var median = cosine.median;
// returns 2.0

var s2 = cosine.variance;
// returns ~2.091

var y = cosine.cdf( 0.8 );
// returns ~0.221
```

</section>

<!-- /.examples -->

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</section>

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</section>

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<section class="main-repo" >

* * *

## 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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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

[cosine-distribution]: https://en.wikipedia.org/wiki/Raised_cosine_distribution

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

[expected-value]: https://en.wikipedia.org/wiki/Expected_value

[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis

[median]: https://en.wikipedia.org/wiki/Median

[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29

[skewness]: https://en.wikipedia.org/wiki/Skewness

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

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

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