Probability Mass Function
Hypergeometric distribution probability mass function (PMF).
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 probability mass function (PMF) for a hypergeometric random variable is given by
Usage
var pmf = require( '@stdlib/stats/base/dists/hypergeometric/pmf' );
pmf( x, N, K, n )
Evaluates the probability mass function (PMF) for a hypergeometric distribution with parameters N
(population size), K
(subpopulation size), and n
(number of draws).
var y = pmf( 1.0, 8, 4, 2 );
// returns ~0.571
y = pmf( 2.0, 8, 4, 2 );
// returns ~0.214
y = pmf( 0.0, 8, 4, 2 );
// returns ~0.214
y = pmf( 1.5, 8, 4, 2 );
// returns 0.0
If provided NaN
as any argument, the function returns NaN
.
var y = pmf( NaN, 10, 5, 2 );
// returns NaN
y = pmf( 0.0, NaN, 5, 2 );
// returns NaN
y = pmf( 0.0, 10, NaN, 2 );
// returns NaN
y = pmf( 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 = pmf( 2.0, 10.5, 5, 2 );
// returns NaN
y = pmf( 2.0, 10, 1.5, 2 );
// returns NaN
y = pmf( 2.0, 10, 5, -2.0 );
// returns NaN
If the number of draws n
exceeds population size N
, the function returns NaN
.
var y = pmf( 2.0, 10, 5, 12 );
// returns NaN
y = pmf( 2.0, 8, 3, 9 );
// returns NaN
pmf.factory( N, K, n )
Returns a function for evaluating the probability mass function (PMF) of a hypergeometric distribution with parameters N
(population size), K
(subpopulation size), and n
(number of draws).
var mypmf = pmf.factory( 30, 20, 5 );
var y = mypmf( 4.0 );
// returns ~0.34
y = mypmf( 1.0 );
// returns ~0.029
Examples
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var pmf = require( '@stdlib/stats/base/dists/hypergeometric/pmf' );
var i;
var N;
var K;
var n;
var x;
var y;
for ( i = 0; i < 10; i++ ) {
x = round( randu() * 5.0 );
N = round( randu() * 20.0 );
K = round( randu() * N );
n = round( randu() * N );
y = pmf( x, N, K, n );
console.log( 'x: %d, N: %d, K: %d, n: %d, P(X=x;N,K,n): %d', x, N, K, n, y.toFixed( 4 ) );
}