Probability Density Function

F distribution probability density function (PDF).

The probability density function (PDF) for a F random variable is

f left-parenthesis x semicolon d 1 comma d 2 right-parenthesis equals StartStartFraction StartRoot StartFraction left-parenthesis d 1 x right-parenthesis Superscript d 1 Baseline d 2 Superscript d 2 Baseline Over left-parenthesis d 1 x plus d 2 right-parenthesis Superscript d 1 plus d 2 Baseline EndFraction EndRoot OverOver x normal upper B left-parenthesis StartFraction d 1 Over 2 EndFraction comma StartFraction d 2 Over 2 EndFraction right-parenthesis EndEndFraction

where d1 is the numerator degrees of freedom and d2 is the denominator degrees of freedom and B is the Beta function.

Usage

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

pdf( x, d1, d2 )

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

var y = pdf( 2.0, 0.5, 1.0 );
// returns ~0.057

y = pdf( 0.1, 1.0, 1.0 );
// returns ~0.915

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

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

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

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

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

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

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

y = pdf( 2.0, -1.0, 1.0 );
// returns NaN

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

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

y = pdf( 2.0, 1.0, -1.0 );
// returns NaN

pdf.factory( d1, d2 )

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

var mypdf = pdf.factory( 6.0, 7.0 );
var y = mypdf( 7.0 );
// returns ~0.004

y = mypdf( 2.0 );
// returns ~0.166

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    x = randu() * 4.0;
    d1 = randu() * 10.0;
    d2 = randu() * 10.0;
    y = pdf( 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 ) );
}