Quantile Function

Gamma distribution quantile function.

The quantile function for a gamma random variable is

for 0 <= p < 1, where alpha is the shape parameter and beta is the rate parameter of the distribution. P^{-1} is the inverse of the lower regularized incomplete gamma function.

Installation

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

Usage

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

quantile( p, alpha, beta )

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

var y = quantile( 0.8, 2.0, 1.0 );
// returns ~2.994

y = quantile( 0.5, 4.0, 2.0 );
// returns ~1.836

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( 0.0, NaN, 1.0 );
// returns NaN

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

If provided alpha < 0, the function returns NaN.

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

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

var y = quantile( 0.3, 0.0, 2.0 );
// returns 0.0

y = quantile( 0.9, 0.0, 2.0 );
// returns 0.0

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

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

quantile.factory( alpha, beta )

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

var myquantile = quantile.factory( 2.0, 2.0 );
var y = myquantile( 0.8 );
// returns ~1.497

y = myquantile( 0.4 );
// returns ~0.688

Examples

var randu = require( '@stdlib/random-base-randu' );
var quantile = require( '@stdlib/stats-base-dists-gamma-quantile' );

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

for ( i = 0; i < 20; i++ ) {
    p = randu();
    alpha = randu() * 5.0;
    beta = randu() * 5.0;
    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.