Quantile Function

Studentized range distribution quantile function.

Usage

var quantile = require( '@stdlib/stats/base/dists/studentized-range/quantile' );

quantile( p, r, v[, nranges=1] )

Evaluates the quantile function for a studentized range distribution with sample size r and v degrees of freedom. Optionally. Optionally, the number of groups whose maximum range is considered can be specified via the nranges parameter.

var y = quantile( 0.5, 3.0, 2.0 );
// returns ~0.0644

y = quantile( 0.9, 17.0, 2.0 );
// returns ~0.913

y = quantile( 0.5, 3.0, 2.0, 2 );
// returns ~0.01

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

var y = quantile( 1.9, 3.0, 2.0 );
// returns NaN

y = quantile( -0.1, 3.0, 2.0 );
// returns NaN

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

var y = quantile( NaN, 2.0, 2.0 );
// returns NaN

y = quantile( 0.0, NaN, 2.0 );
// returns NaN

If provided v < 2 or r < 2, the function returns NaN.

var y = quantile( 0.4, -1.0, 3.0 );
// returns NaN

y = quantile( 0.4, 3.0, 1.5 );
// returns NaN

quantile.factory( r, v[, nranges=1] )

Returns a function for evaluating the quantile function of an studentized range distribution with sample size r and v degrees of freedom. Optionally, the number of groups whose maximum range is considered can be specified via the nranges parameter.

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/stats/base/dists/studentized-range/quantile' );

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

for ( i = 0; i < 10; i++ ) {
    p = randu();
    r = ( randu() * 20.0 ) + 2.0;
    v = ( randu() * 20.0 ) + 2.0;
    y = quantile( p, r, v );
    console.log( 'p: %d, r: %d, v: %d, Q(p;r,v): %d', p.toFixed( 4 ), r.toFixed( 4 ), v.toFixed( 4 ), y.toFixed( 4 ) );
}