Quantile Function

Discrete uniform distribution quantile function.

The quantile function for a discrete uniform random variable is

upper Q left-parenthesis p right-parenthesis equals a plus left floor p dot left-parenthesis b minus a plus 1 right-parenthesis right floor

for 0 <= p <= 1, where a is the minimum support and b is the maximum support. The parameters must satisfy a <= b.

Usage

var quantile = require( '@stdlib/math/base/dists/discrete-uniform/quantile' );

quantile( p, a, b )

Evaluates the quantile function for a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var y = quantile( 0.8, 0, 1 );
// returns 1

y = quantile( 0.5, 0, 10 );
// returns 5

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

var y = quantile( 1.9, 0, 2 );
// returns NaN

y = quantile( -0.1, 0, 2 );
// returns NaN

If a or b is not an integer value, the function returns NaN.

var y = quantile( 0.2, 1, 5.5 );
// returns NaN

If provided a > b, the function returns NaN.

var y = quantile( 0.4, 2, 1 );
// returns NaN

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

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

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

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

quantile.factory( a, b )

Returns a function for evaluating the quantile function of a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var myquantile = quantile.factory( 0, 4 );
var y = myquantile( 0.8 );
// returns 4

y = myquantile( 0.3 );
// returns 1

Examples

var randint = require( '@stdlib/random/base/discrete-uniform' );
var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/math/base/dists/discrete-uniform/quantile' );

var randa = randint.factory( 0, 5 );
var randb = randint.factory();
var a;
var b;
var p;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    a = randa();
    b = randb( a, a+randa() );
    v = quantile( p, a, b );
    console.log( 'p: %d, a: %d, b: %d, Q(p;a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}