Cumulative Distribution Function

Chi distribution cumulative distribution function.

The cumulative distribution function for a chi random variable is

upper F left-parenthesis x semicolon k right-parenthesis equals upper P left-parenthesis k slash 2 comma x squared slash 2 right-parenthesis

where k is the degrees of freedom and P is the lower regularized incomplete gamma function.

Usage

var cdf = require( '@stdlib/math/base/dists/chi/cdf' );

cdf( x, k )

Evaluates the cumulative distribution function (CDF) for a chi distribution with degrees of freedom k.

var y = cdf( 2.0, 1.0 );
// returns ~0.954

y = cdf( 2.0, 3.0 );
// returns ~0.739

y = cdf( 1.0, 0.5 );
// returns ~0.846

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

y = cdf( -Infinity, 4.0 );
// returns 0.0

y = cdf( +Infinity, 4.0 );
// returns 1.0

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

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

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

If provided k < 0, the function returns NaN.

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

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

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

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

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

cdf.factory( k )

Returns a function for evaluating the cumulative distribution function for a chi distribution with degrees of freedom k.

var mycdf = cdf.factory( 3.0 );

var y = mycdf( 6.0 );
// returns ~1.0

y = mycdf( 1.5 );
// returns ~0.478

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var cdf = require( '@stdlib/math/base/dists/chi/cdf' );

var k;
var x;
var y;
var i;

for ( i = 0; i < 20; i++ ) {
    x = randu() * 10.0;
    k = round( randu()*5.0 );
    y = cdf( x, k );
    console.log( 'x: %d, k: %d, F(x;k): %d', x.toFixed( 4 ), k.toFixed( 4 ), y.toFixed( 4 ) );
}