Quantile Function

Rayleigh distribution quantile function.

The quantile function for a Rayleigh random variable is

upper Q left-parenthesis p semicolon sigma right-parenthesis equals sigma StartRoot minus ln left-bracket left-parenthesis 1 minus p right-parenthesis squared right-bracket EndRoot

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

Usage

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

quantile( p, sigma )

Evaluates the quantile function for a Rayleigh distribution with parameter sigma (scale parameter).

var y = quantile( 0.8, 1.0 );
// returns ~1.794

y = quantile( 0.5, 4.0 );
// returns ~4.71

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

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

y = quantile( -0.1, 1.0 );
// returns NaN

If provided NaN as any argument, the function returns NaN.

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

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

If provided sigma < 0, the function returns NaN.

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

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

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

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

quantile.factory( sigma )

Returns a function for evaluating the quantile function of a Rayleigh distribution with scale parameter sigma.

var myQuantile = quantile.factory( 0.4 );

y = myQuantile( 0.4 );
// returns ~0.404

y = myQuantile( 1.0 );
// returns Infinity

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    p = randu();
    sigma = randu() * 10.0;
    y = quantile( p, sigma );
    console.log( 'p: %d, σ: %d, Q(p;σ): %d', p.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}