Quantile Function

Cauchy distribution quantile function.

The quantile function for a Cauchy random variable is

for 0 <= p <= 1, where x0 is the location parameter and gamma > 0 is the scale parameter.

Installation

npm install @stdlib/stats-base-dists-cauchy-quantile

Usage

var quantile = require( '@stdlib/stats-base-dists-cauchy-quantile' );

quantile( p, x0, gamma )

Evaluates the quantile function for a Cauchy distribution with parameters x0 (location parameter) and gamma > 0 (scale parameter).

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

y = quantile( 0.2, 4.0, 2.0 );
// returns ~1.247

y = quantile( 0.9, 4.0, 2.0 );
// returns ~10.155

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 gamma <= 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( x0, gamma )

Returns a function for evaluating the quantile function of a Cauchy distribution with location parameter x0 and scale parameter gamma > 0.

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

var y = myquantile( 0.2 );
// returns ~7.247

y = myquantile( 0.8 );
// returns ~12.753

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var quantile = require( '@stdlib/stats-base-dists-cauchy-quantile' );

var gamma;
var x0;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    x0 = ( randu()*10.0 ) - 5.0;
    gamma = ( randu()*20.0 ) + EPS;
    y = quantile( p, gamma, x0 );
    console.log( 'p: %d, x0: %d, γ: %d, Q(p;x0,γ): %d', p.toFixed(4), x0.toFixed(4), gamma.toFixed(4), y.toFixed(4) );
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.