Cumulative Distribution Function

Hypergeometric distribution cumulative distribution 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 cumulative distribution function for a hypergeometric random variable is

Installation

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

Usage

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

cdf( x, N, K, n )

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

var y = cdf( 1.0, 8, 4, 2 );
// returns ~0.786

y = cdf( 1.5, 8, 4, 2 );
// returns ~0.786

y = cdf( 2.0, 8, 4, 2 );
// returns 1.0

y = cdf( 0.0, 8, 4, 2);
// returns ~0.214

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

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

y = cdf( 0.0, NaN, 5, 2 );
// returns NaN

y = cdf( 0.0, 10, NaN, 2 );
// returns NaN

y = cdf( 0.0, 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 = cdf( 2.0, 10.5, 5, 2 );
// returns NaN

y = cdf( 2.0, 10, 1.5, 2 );
// returns NaN

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

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

var y = cdf( 2.0, 10, 5, 12 );
// returns NaN

y = cdf( 2.0, 8, 3, 9 );
// returns NaN

cdf.factory( N, K, n )

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

var mycdf = cdf.factory( 30, 20, 5 );
var y = mycdf( 4.0 );
// returns ~0.891

y = mycdf( 1.0 );
// returns ~0.031

Examples

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

var i;
var N;
var K;
var n;
var x;
var y;

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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.