Quantile Function

Student's t distribution quantile function.

The quantile function for a Student's t random variable is

upper Q left-parenthesis p semicolon nu right-parenthesis equals inf left-brace x element-of double-struck upper R colon p less-than-or-equal-to upper F left-parenthesis x semicolon nu right-parenthesis right-brace

for 0 <= p <= 1, where v > 0 is the degrees of freedom.

Usage

var quantile = require( '@stdlib/math/base/dists/t/quantile' );

quantile( p, v )

Evaluates the quantile function for a Student's t distribution with degrees of freedom v.

var y = quantile( 0.8, 1.0 );
// returns ~1.376

y = quantile( 0.1, 1.0 );
// returns ~-3.078

y = quantile( 0.5, 0.1 );
// returns 0.0

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( 0.0, NaN );
// returns NaN

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

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

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

quantile.factory( v )

Returns a function for evaluating the quantile function of an Student's t distribution with degrees of freedom v.

var myquantile = quantile.factory( 4.0 );

var y = myquantile( 0.2 );
// returns ~-0.941

y = myquantile( 0.9 );
// returns ~1.533

Examples

var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/math/base/dists/t/quantile' );

var v;
var p;
var y;
var i;

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