Quantile Function

F distribution quantile function.

The quantile function for a F random variable is

upper Q left-parenthesis p semicolon d 1 comma d 2 right-parenthesis equals inf left-brace x element-of left-bracket 0 comma plus normal infinity right-parenthesis colon p less-than-or-equal-to upper F left-parenthesis x semicolon d 1 comma d 2 right-parenthesis right-brace

for 0 <= p < 1, where d1 is the numerator degrees of freedom, d2 is the denominator degrees of freedom and F the cumulative distribution function (CDF) of the F distribution.

Usage

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

quantile( p, d1, d2 )

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

var y = quantile( 0.5, 1.0, 1.0 );
// returns 1.0

y = quantile( 0.2, 4.0, 2.0 );
// returns ~0.405

y = quantile( 0.8, 4.0, 2.0 );
// returns ~4.236

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

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

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

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

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

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

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

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

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

y = quantile( 0.4, 0.0, 1.0 );
// returns NaN

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

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

y = quantile( 0.4, 1.0, 0.0 );
// returns NaN

quantile.factory( d1, d2 )

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

var myquantile = quantile.factory( 10.0, 2.0 );

var y = myquantile( 0.2 );
// returns ~0.527

y = myquantile( 0.8 );
// returns ~4.382

Examples

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

var d1;
var d2;
var p;
var y;
var i;

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