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Probability Density Function
F distribution probability density function (PDF).
The probability density function (PDF) for a F random variable is
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/stats/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/stats/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 ) );
}