npm package: @stdlib/stats-base-dists-degenerate-cdf
Description: Degenerate distribution cumulative distribution function (CDF).
Author: The Stdlib Authors
Latest version: 0.3.1

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# 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] -->

> [Degenerate distribution][degenerate-distribution] [cumulative distribution function][cdf].

<section class="intro">

The [cumulative distribution function][cdf] for a [degenerate][degenerate-distribution] random variable is

<!-- <equation class="equation" label="eq:degenerate_cdf" align="center" raw="F(x;\mu)={\begin{cases}1, & x \geq \mu,\\0,& x < \mu.\end{cases}}" alt="Cumulative distribution function for a degenerate distribution."> -->

<div class="equation" align="center" data-raw-text="F(x;\mu)={\begin{cases}1, &amp; x \geq \mu,\\0,&amp; x &lt; \mu.\end{cases}}" data-equation="eq:degenerate_cdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/degenerate/cdf/docs/img/equation_degenerate_cdf.svg" alt="Cumulative distribution function for a degenerate distribution.">
    <br>
</div>

<!-- </equation> -->

where `µ` is the constant value of the distribution.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-degenerate-cdf
```

</section>

<section class="usage">

## Usage

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

#### cdf( x, mu )

Evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.

```javascript
var y = cdf( 2.0, 8.0 );
// returns 0.0

y = cdf( 8.0, 8.0 );
// returns 1.0

y = cdf( 10.0, 8.0 );
// returns 1.0
```

#### cdf.factory( mu )

Returns a function for evaluating the [cumulative distribution function][cdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.

```javascript
var mycdf = cdf.factory( 10.0 );

var y = mycdf( 10.0 );
// returns 1.0

y = mycdf( 8.0 );
// returns 0.0
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

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

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 10, opts );
var mu = discreteUniform( 10, 0, 10, opts );

logEachMap( 'x: %d, µ: %d, F(x;µ): %0.4f', x, mu, cdf );
```

</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/degenerate/cdf.h"
```

#### stdlib_base_dists_degenerate_cdf( x, mu )

Evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.

```c
double y = stdlib_base_dists_degenerate_cdf( 2.0, 3.0 );
// returns 0.0
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.
-   **mu**: `[in] double` constant value of distribution.

```c
double stdlib_base_dists_degenerate_cdf( const double x, const double mu );
```

</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/degenerate/cdf.h"
#include "stdlib/math/base/special/round.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 mu;
    double x;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
        mu = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
        y = stdlib_base_dists_degenerate_cdf( x, mu );
        printf( "x: %lf, µ: %lf, F(x;µ): %lf\n", x, mu, 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 -->

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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-degenerate-cdf/main/LICENSE

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

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution

</section>

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