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
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 ) );
}