Quantile Function

Lognormal distribution quantile function.

The quantile function for a lognormal random variable is

upper Q left-parenthesis p semicolon mu comma sigma right-parenthesis equals exp left-parenthesis mu plus sigma normal upper Phi Superscript negative 1 Baseline left-parenthesis p right-parenthesis right-parenthesis

for 0 <= p < 1, where mu is the location parameter and sigma > 0 is the scale parameter.

Usage

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

quantile( p, mu, sigma )

Evaluates the quantile function for a lognormal distribution with parameters mu (location parameter) and sigma (scale parameter).

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

y = quantile( 0.5, 4.0, 1.0 );
// returns ~54.598

y = quantile( 0.8, 4.0, 1.0 );
// returns ~126.675

y = quantile( 0.8, 4.0, 4.0 );
// returns ~1582.063

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

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

quantile.factory( mu, sigma )

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

var myquantile = quantile.factory( 4.0, 2.0 );

var y = myquantile( 0.2 );
// returns ~10.143

y = myquantile( 0.8 );
// returns ~293.901

Examples

var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/math/base/dists/lognormal/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.toFixed( 4 ), mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}