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Quantile Function

Hypergeometric distribution quantile function.

Imagine a scenario with a population of size N, of which a subpopulation of size K can be considered successes. We draw n observations from the total population. Defining the random variable X as the number of successes in the n draws, X is said to follow a hypergeometric distribution.

The quantile function for a hypergeometric random variable returns for any 0 <= p <= 1 the value x for which

$$F(x-1;N,K,n) < p \le F(x;N,K,n)$$

where F is the cumulative distribution function (CDF) of a hypergeometric random variable with parameters N, K and n, where N is the population size, K is the subpopulation size, and n is the number of draws.

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

quantile( p, N, K, n )

Evaluates the quantile function for a hypergeometric distribution with parameters N (population size), K (subpopulation size), and n (number of draws).

var y = quantile( 0.5, 8, 4, 2 );
// returns 1

y = quantile( 0.9, 120, 80, 20 );
// returns 16

y = quantile( 0.0, 120, 80, 50 );
// returns 10

y = quantile( 0.0, 8, 4, 2 );
// returns 0

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

var y = quantile( NaN, 10, 5, 2 );
// returns NaN

y = quantile( 0.4, NaN, 5, 2 );
// returns NaN

y = quantile( 0.4, 10, NaN, 2 );
// returns NaN

y = quantile( 0.4, 10, 5, NaN );
// returns NaN

If provided a population size N, subpopulation size K or draws n which is not a nonnegative integer, the function returns NaN.

var y = quantile( 0.2, 6.5, 5, 2 );
// returns NaN

y = quantile( 0.2, 5, 1.5, 2 );
// returns NaN

y = quantile( 0.2, 10, 5, -2.0 );
// returns NaN

If the number of draws n or the subpopulation size K exceed population size N, the function returns NaN.

var y = quantile( 0.2, 10, 5, 12 );
// returns NaN

y = quantile( 0.2, 8, 3, 9 );
// returns NaN

quantile.factory( N, K, n )

Returns a function for evaluating the quantile function for a hypergeometric distribution with parameters N (population size), K (subpopulation size), and n (number of draws).

var myquantile = quantile.factory( 100, 20, 10 );
var y = myquantile( 0.2 );
// returns 1

y = myquantile( 0.9 );
// returns 4

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var quantile = require( '@stdlib/stats-base-dists-hypergeometric-quantile' );

var i;
var N;
var K;
var n;
var p;
var y;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    N = round( randu() * 20 );
    K = round( randu() * N );
    n = round( randu() * K );
    y = quantile( p, N, K, n );
    console.log( 'p: %d, N: %d, K: %d, n: %d, Q(p;N,K,n): %d', p.toFixed( 4 ), N, K, n, y.toFixed( 4 ) );
}

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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

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Copyright

Copyright © 2016-2024. The Stdlib Authors.