Cumulative Distribution Function

Normal distribution cumulative distribution function.

The cumulative distribution function for a normal random variable is

where µ is the mean and σ is the standard deviation.

Installation

npm install @stdlib/stats-base-dists-normal-cdf

Usage

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

cdf( x, mu, sigma )

Evaluates the cumulative distribution function (CDF) for a normal distribution with parameters mu (mean) and sigma (standard deviation).

var y = cdf( 2.0, 0.0, 1.0 );
// returns ~0.977

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

y = cdf( -1.0, 4.0, 2.0 );
// returns ~0.006

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 sigma < 0, the function returns NaN.

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

If provided sigma = 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, sigma )

Returns a function for evaluating the cumulative distribution function of a normal distribution with parameters mu and sigma.

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

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

y = mycdf( 8.0 );
// returns ~0.159

Examples

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

var sigma;
var mu;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    mu = (randu() * 10.0) - 5.0;
    sigma = randu() * 20.0;
    y = cdf( x, mu, sigma );
    console.log( 'x: %d, µ: %d, σ: %d, F(x;µ,σ): %d', x, mu, sigma, 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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.