# 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.

## Usage

var cdf = require( '@stdlib/math/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/math/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 );
}