Cumulative Distribution Function

F distribution cumulative distribution function.

The cumulative distribution function for a F random variable is

upper F left-parenthesis x semicolon d 1 comma d 2 right-parenthesis equals upper I Subscript StartFraction d 1 x Over d 1 x plus d 2 EndFraction Baseline left-parenthesis StartFraction d 1 Over 2 EndFraction comma StartFraction d 2 Over 2 EndFraction right-parenthesis

where d1 is the numerator degrees of freedom, d2 is the denominator degrees of freedom and I_{x}(a,b) is the lower regularized incomplete beta function.

Usage

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

cdf( x, d1, d2 )

Evaluates the cumulative distribution function (CDF) for a F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

var y = cdf( 2.0, 1.0, 1.0 );
// returns ~0.608

y = cdf( 2.0, 8.0, 4.0 );
// returns ~0.737

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

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

y = cdf( +Infinity, 4.0, 2.0 );
// returns 1.0

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

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

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

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

If provided d1 <= 0, the function returns NaN.

var y = cdf( 2.0, -1.0, 0.5 );
// returns NaN

y = cdf( 2.0, 0.0, 0.5 );
// returns NaN

If provided d2 <= 0, the function returns NaN.

var y = cdf( 2.0, 0.5, -1.0 );
// returns NaN

y = cdf( 2.0, 0.5, 0.0 );
// returns NaN

cdf.factory( d1, d2 )

Returns a function for evaluating the cumulative distribution function of a F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

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

var y = mycdf( 10.0 );
// returns ~0.906

y = mycdf( 8.0 );
// returns ~0.884

Examples

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

var d1;
var d2;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    d1 = randu() * 10.0;
    d2 = randu() * 10.0;
    y = cdf( x, d1, d2 );
    console.log( 'x: %d, d1: %d, d2: %d, F(x;d1,d2): %d', x.toFixed( 4 ), d1.toFixed( 4 ), d2.toFixed( 4 ), y.toFixed( 4 ) );
}