Ninety-nine Pitchers of Malt

# npm

## @stdlib/stats-base-dists-cosine-cdf

0.0.6 • Public • Published

# Cumulative Distribution Function

Raised cosine distribution cumulative distribution function.

The cumulative distribution function for a raised cosine random variable is

where `μ` is the location parameter and `s > 0` is the scale parameter.

## Installation

`npm install @stdlib/stats-base-dists-cosine-cdf`

## Usage

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

#### cdf( x, mu, s )

Evaluates the cumulative distribution function (CDF) for a raised cosine distribution with parameters `mu` (location parameter) and `s` (scale parameter).

```var y = cdf( 2.0, 0.0, 3.0 );
// returns ~0.971

y = cdf( 0.0, 0.0, 1.0 );
// returns ~0.5

y = cdf( -1.0, 4.0, 2.0 );
// returns 0.0```

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

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

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

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

If provided `s < 0`, the function returns `NaN`.

```var y = cdf( 2.0, 0.0, -1.0 );
// returns NaN```

If provided `s = 0`, the function evaluates the CDF of a degenerate distribution centered at `mu`.

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

y = cdf( 8.0, 8.0, 0.0 );
// returns 1.0

y = cdf( 10.0, 8.0, 0.0 );
// returns 1.0```

#### cdf.factory( mu, s )

Returns a function for evaluating the cumulative distribution function of a raised cosine distribution with parameters `mu` (location parameter) and `s` (scale parameter).

```var mycdf = cdf.factory( 10.0, 2.0 );

var y = mycdf( 10.0 );
// returns 0.5

y = mycdf( 8.0 );
// returns 0.0

y = mycdf( 12.0 );
// returns 1.0```

## Examples

```var randu = require( '@stdlib/random-base-randu' );
var cdf = require( '@stdlib/stats-base-dists-cosine-cdf' );

var mu;
var s;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
x = randu() * 10.0;
mu = randu() * 10.0;
s = randu() * 10.0;
y = cdf( x, mu, s );
console.log( 'x: %d, µ: %d, s: %d, F(x;µ,s): %d', x, mu, s, y );
}```

## Notice

This package is part of 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, see the main project repository.

### Install

`npm i @stdlib/stats-base-dists-cosine-cdf`

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