Quantile Function

Degenerate distribution quantile function.

The quantile function for a degenerate random variable is

upper Q left-parenthesis p semicolon mu 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 mu right-parenthesis right-brace equals mu

for 0 <= p <= 1 and where µ is the constant value of the distribution.

Usage

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

quantile( p, mu )

Evaluates the quantile function of a degenerate distribution centered at mu.

var y = quantile( 0.3, 8.0 );
// returns 8.0

y = quantile( 0.9, 8.0 );
// returns 8.0

quantile.factory( mu )

Returns a function for evaluating the quantile function of a degenerate distribution centered at mu.

var myquantile = quantile.factory( 10.0 );

var y = myquantile( 0.2 );
// returns 10.0

y = myquantile( 1.1 );
// returns NaN

Examples

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

var mu;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    mu = ( randu()*10.0 ) - 5.0;
    y = quantile( p, mu );
    console.log( 'p: %d, µ: %d, Q(p;µ): %d', p, mu, y );
}