npm package: @stdlib/stats-base-dists-arcsine-logcdf
Description: Arcsine distribution logarithm of cumulative distribution function (CDF).
Author: The Stdlib Authors
Latest version: 0.2.3

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# Logarithm of Cumulative Distribution Function

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

> [Arcsine][arcsine-distribution] distribution logarithm of [cumulative distribution function][cdf].

<section class="intro">

The [cumulative distribution function][cdf] for an [arcsine][arcsine-distribution] random variable is

<!-- <equation class="equation" label="eq:arcsine_cdf" align="center" raw="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" alt="Cumulative distribution function for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" data-equation="eq:arcsine_cdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/logcdf/docs/img/equation_arcsine_cdf.svg" alt="Cumulative distribution function for an arcsine distribution.">
    <br>
</div>

<!-- </equation> -->

where `a` is the minimum support and `b` is the maximum support. The parameters must satisfy `a < b`.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-arcsine-logcdf
```

</section>

<section class="usage">

## Usage

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

#### logcdf( x, a, b )

Evaluates the logarithm of the [cumulative distribution function][cdf] (CDF) for an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).

```javascript
var y = logcdf( 9.0, 0.0, 10.0 );
// returns ~-0.23

y = logcdf( 0.5, 0.0, 2.0 );
// returns ~-1.1

y = logcdf( -Infinity, 2.0, 4.0 );
// returns -Infinity

y = logcdf( +Infinity, 2.0, 4.0 );
// returns 0.0
```

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

```javascript
var y = logcdf( NaN, 0.0, 1.0 );
// returns NaN

y = logcdf( 0.0, NaN, 1.0 );
// returns NaN

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

If provided `a >= b`, the function returns `NaN`.

```javascript
var y = logcdf( 1.0, 2.5, 2.0 );
// returns NaN
```

#### logcdf.factory( a, b )

Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).

```javascript
var mylogcdf = logcdf.factory( 0.0, 10.0 );
var y = mylogcdf( 0.5 );
// returns ~-1.941

y = mylogcdf( 8.0 );
// returns ~-0.35
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   In virtually all cases, using the `logpdf` or `logcdf` functions is preferable to manually computing the logarithm of the `pdf` or `cdf`, respectively, since the latter is prone to overflow and underflow.

</section>

<!-- /.notes -->

<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 logcdf = require( '@stdlib/stats-base-dists-arcsine-logcdf' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 25, -10.0, 10.0, opts );
var a = uniform( x.length, -20.0, 0.0, opts );
var b = uniform( x.length, 0.0, 40.0, opts );

logEachMap( 'x: %0.4f, a: %0.4f, b: %0.4f, ln(F(x;a,b)): %0.4f', x, a, b, logcdf );
```

</section>

<!-- /.examples -->

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

<section class="related">

</section>

<!-- /.related -->

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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].

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

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

</section>

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