Quantile Function

Laplace distribution quantile function.

The quantile function for a Laplace random variable is

upper Q left-parenthesis p right-parenthesis equals mu minus b s g n left-parenthesis p minus 0.5 right-parenthesis ln left-parenthesis 1 minus 2 StartAbsoluteValue p minus 0.5 EndAbsoluteValue right-parenthesis

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

Usage

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

quantile( p, mu, b )

Evaluates the quantile function for a Laplace distribution with parameters mu (location parameter) and b > 0 (scale parameter).

var y = quantile( 0.8, 0.0, 1.0 );
// returns ~0.916

y = quantile( 0.5, 4.0, 2.0 );
// returns 4

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 b <= 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, b )

Returns a function for evaluating the quantile function of a Laplace distribution with parameters mu and b > 0.

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

var y = myquantile( 0.5 );
// returns 10.0

y = myquantile( 0.8 );
// returns ~11.833

Examples

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

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

for ( i = 0; i < 100; i++ ) {
    p = randu();
    mu = randu() * 10.0;
    b = randu() * 10.0;
    y = quantile( p, mu, b );
    console.log( 'p: %d, µ: %d, b: %d, Q(p;µ,b): %d', p.toFixed( 4 ), mu.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}