Quantile Function

Beta distribution quantile function.

The quantile function for a beta random variable is

for 0 <= p <= 1, where alpha > 0 is the first shape parameter and beta > 0 is the second shape parameter and F(x;alpha,beta) denotes the cumulative distribution function of a beta random variable with parameters alpha and beta.

Installation

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

Usage

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

quantile( p, alpha, beta )

Evaluates the quantile function for a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var y = quantile( 0.8, 2.0, 1.0 );
// returns ~0.894

y = quantile( 0.5, 4.0, 2.0 );
// returns ~0.686

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

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

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

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

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

y = quantile( 0.5, NaN, 1.0 );
// returns NaN

y = quantile( 0.5, 1.0, NaN );
// returns NaN

If provided alpha <= 0, the function returns NaN.

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

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

If provided beta <= 0, the function returns NaN.

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

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

quantile.factory( alpha, beta )

Returns a function for evaluating the quantile function of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

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

var y = myquantile( 0.8 );
// returns ~0.713

y = myquantile( 0.4 );
// returns ~0.433

Examples

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

var alpha;
var beta;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    alpha = ( randu()*5.0 ) + EPS;
    beta = ( randu()*5.0 ) + EPS;
    y = quantile( p, alpha, beta );
    console.log( 'p: %d, α: %d, β: %d, Q(p;α,β): %d', p.toFixed( 4 ), alpha.toFixed( 4 ), beta.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.