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Probability Density Function
Chi distribution probability density function (PDF).
The probability density function (PDF) for a chi random variable is
where k
is the degrees of freedom and Γ
denotes the gamma function.
Usage
var pdf = require( '@stdlib/stats/base/dists/chi/pdf' );
pdf( x, k )
Evaluates the probability density function (PDF) for a chi distribution with degrees of freedom k
.
var y = pdf( 0.1, 1.0 );
// returns ~0.794
y = pdf( 0.5, 2.0 );
// returns ~0.441
y = pdf( -1.0, 4.0 );
// returns 0.0
If provided NaN
as any argument, the function returns NaN
.
var y = pdf( NaN, 1.0 );
// returns NaN
y = pdf( 0.0, NaN );
// returns NaN
If provided k < 0
, the function returns NaN
.
var y = pdf( 2.0, -2.0 );
// returns NaN
If provided k = 0
, the function evaluates the PDF of a degenerate distribution centered at 0
.
var y = pdf( 2.0, 0.0 );
// returns 0.0
y = pdf( 0.0, 0.0 );
// returns Infinity
pdf.factory( k )
Returns a function
for evaluating the PDF for a chi distribution with degrees of freedom k
.
var myPDF = pdf.factory( 6.0 );
var y = myPDF( 3.0 );
// returns ~0.337
y = myPDF( 1.0 );
// returns ~0.076
Examples
var randu = require( '@stdlib/random/base/randu' );
var pdf = require( '@stdlib/stats/base/dists/chi/pdf' );
var k;
var x;
var y;
var i;
for ( i = 0; i < 20; i++ ) {
x = randu() * 10.0;
k = randu() * 10.0;
y = pdf( x, k );
console.log( 'x: %d, k: %d, f(x;k): %d', x.toFixed( 4 ), k.toFixed( 4 ), y.toFixed( 4 ) );
}