Quantile Function

Chi-squared distribution quantile function.

The quantile function for a chi-squared random variable is

upper Q left-parenthesis p semicolon k right-parenthesis equals 2 dot upper P Superscript negative 1 Baseline left-parenthesis p comma k slash 2 right-parenthesis

for 0 <= p < 1, where k is the degrees of freedom and P^{-1} is the inverse of the lower, regularized incomplete gamma function.

Usage

var quantile = require( '@stdlib/math/base/dists/chisquare/quantile' );

quantile( p, k )

Evaluates the quantile function for a chi-squared distribution with degrees of freedom k.

var y = quantile( 0.8, 1.0 );
// returns ~1.642

y = quantile( 0.5, 4.0 );
// returns ~3.357

y = quantile( 0.8, 0.1 );
// returns ~0.014

If provided a probability p outside the interval [0,1], the function returns NaN.

var y = quantile( 1.9, 1.0 );
// returns NaN

y = quantile( -0.1, 1.0 );
// returns NaN

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

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

y = quantile( 0.2, NaN );
// returns NaN

If provided k < 0, the function returns NaN.

var y = quantile( 0.4, -1.0 );
// returns NaN

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

var y = quantile( 0.3, 0.0 );
// returns 0.0

y = quantile( 0.9, 0.0 );
// returns 0.0

quantile.factory( k )

Returns a function for evaluating the quantile function of a chi-squared distribution with degrees of freedom k.

var myquantile = quantile.factory( 0.4 );

var y = myquantile( 0.9 );
// returns ~1.21

y = myquantile( 1.0 );
// returns Infinity

Examples

var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/math/base/dists/chisquare/quantile' );

var k;
var p;
var y;
var i;

for ( i = 0; i < 20; i++ ) {
    p = randu();
    k = randu() * 10.0;
    y = quantile( p, k );
    console.log( 'p: %d, k: %d, Q(p;k): %d', p.toFixed( 4 ), k.toFixed( 4 ), y.toFixed( 4 ) );
}