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

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# Arcsine

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> Arcsine 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-arcsine-ctor
```

</section>

<section class="usage">

## Usage

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

#### Arcsine( \[a, b] )

Returns an [arcsine][arcsine-distribution] distribution object.

```javascript
var arcsine = new Arcsine();

var mu = arcsine.mean;
// returns 0.5
```

By default, `a = 0.0` and `b = 1.0`. To create a distribution having a different `a` (minimum support) and `b` (maximum support), provide the corresponding arguments.

```javascript
var arcsine = new Arcsine( 2.0, 4.0 );

var mu = arcsine.mean;
// returns 3.0
```

* * *

## arcsine

An [arcsine][arcsine-distribution] distribution object has the following properties and methods...

### Writable Properties

#### arcsine.a

Minimum support of the distribution. `a` **must** be a number less than `b`.

```javascript
var arcsine = new Arcsine();

var a = arcsine.a;
// returns 0.0

arcsine.a = 0.5;

a = arcsine.a;
// returns 0.5
```

#### arcsine.b

Maximum support of the distribution. `b` **must** be a number greater than `a`.

```javascript
var arcsine = new Arcsine( 2.0, 4.0 );

var b = arcsine.b;
// returns 4.0

arcsine.b = 3.0;

b = arcsine.b;
// returns 3.0
```

* * *

### Computed Properties

#### Arcsine.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var arcsine = new Arcsine( 4.0, 12.0 );

var entropy = arcsine.entropy;
// returns ~1.838
```

#### Arcsine.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var arcsine = new Arcsine( 4.0, 12.0 );

var kurtosis = arcsine.kurtosis;
// returns -1.5
```

#### Arcsine.prototype.mean

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

```javascript
var arcsine = new Arcsine( 4.0, 12.0 );

var mu = arcsine.mean;
// returns 8.0
```

#### Arcsine.prototype.median

Returns the [median][median].

```javascript
var arcsine = new Arcsine( 4.0, 12.0 );

var median = arcsine.median;
// returns 8.0
```

#### Arcsine.prototype.mode

Returns the [mode][mode].

```javascript
var arcsine = new Arcsine( 4.0, 12.0 );

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

#### Arcsine.prototype.skewness

Returns the [skewness][skewness].

```javascript
var arcsine = new Arcsine( 4.0, 12.0 );

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

#### Arcsine.prototype.stdev

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

```javascript
var arcsine = new Arcsine( 4.0, 12.0 );

var s = arcsine.stdev;
// returns ~2.828
```

#### Arcsine.prototype.variance

Returns the [variance][variance].

```javascript
var arcsine = new Arcsine( 4.0, 12.0 );

var s2 = arcsine.variance;
// returns 8.0
```

* * *

### Methods

#### Arcsine.prototype.cdf( x )

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

```javascript
var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.cdf( 2.5 );
// returns ~0.333
```

#### Arcsine.prototype.logcdf( x )

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

```javascript
var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.logcdf( 2.5 );
// returns ~-1.1
```

#### Arcsine.prototype.logpdf( x )

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

```javascript
var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.logpdf( 2.5 );
// returns ~-1.0
```

#### Arcsine.prototype.pdf( x )

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

```javascript
var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.pdf( 2.5 );
// returns ~0.368
```

#### Arcsine.prototype.quantile( p )

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

```javascript
var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.quantile( 0.5 );
// returns 3.0

y = arcsine.quantile( 1.9 );
// returns NaN
```

</section>

<!-- /.usage -->

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<section class="notes">

</section>

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<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

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

var arcsine = new Arcsine( 2.0, 4.0 );

var mu = arcsine.mean;
// returns 3.0

var median = arcsine.median;
// returns 3.0

var s2 = arcsine.variance;
// returns 0.5

var y = arcsine.cdf( 2.5 );
// returns ~0.333
```

</section>

<!-- /.examples -->

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* * *

## 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].

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

[arcsine-distribution]: https://en.wikipedia.org/wiki/Arcsine_distribution

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

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

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

[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[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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