Quantile Function

Normal distribution quantile function.

The quantile function for a normal random variable is

upper Q left-parenthesis p semicolon mu comma sigma right-parenthesis equals mu plus sigma StartRoot 2 EndRoot e r f Superscript negative 1 Baseline left-parenthesis 2 p minus 1 right-parenthesis

for 0 <= p <= 1, where µ is the mean and σ is the standard deviation.

Usage

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

quantile( p, mu, sigma )

Evaluates the quantile function for a normal distribution with parameters mu (mean) and sigma (standard deviation).

var y = quantile( 0.5, 0.0, 1.0 );
// returns 0.0

y = quantile( 0.2, 4.0, 2.0 );
// returns ~2.317

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

var y = quantile( 1.9, 0.0, 1.0 );
// returns NaN

y = quantile( -0.1, 0.0, 1.0 );
// 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

If provided sigma < 0, the function returns NaN.

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

If provided sigma = 0, the function evaluates the quantile function of a degenerate distribution centered at mu.

var y = quantile( 0.3, 8.0, 0.0 );
// returns 8.0

y = quantile( 0.9, 8.0, 0.0 );
// returns 8.0

quantile.factory( mu, sigma )

Returns a function for evaluating the quantile function of a normal distribution with parameters mu and sigma.

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

var y = myquantile( 0.2 );
// returns ~8.317

y = myquantile( 0.8 );
// returns ~11.683

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    p = randu();
    mu = (randu() * 10.0) - 5.0;
    sigma = randu() * 20.0;
    y = quantile( p, mu, sigma );
    console.log( 'p: %d, µ: %d, σ: %d, Q(p;µ,σ): %d', p, mu, sigma, y );
}