Quantile Function

Logistic distribution quantile function.

The quantile function for a logistic random variable is

upper Q left-parenthesis p semicolon mu comma s right-parenthesis equals mu plus s ln left-parenthesis StartFraction p Over 1 minus p EndFraction right-parenthesis

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

Usage

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

quantile( p, mu, s )

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

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

y = quantile( 0.2, 4.0, 2.0 );
// returns ~1.227

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 s < 0, the function returns NaN.

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

If provided s = 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, s )

Returns a function for evaluating the quantile function of a logistic distribution with parameters mu and s.

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

var y = myQuantile( 0.2 );
// returns ~7.227

y = myQuantile( 0.8 );
// returns ~12.773

Examples

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

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

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