README.md

Variance

Hypergeometric distribution variance.

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 variance for a hypergeometric random variable is

$$\mathop{\mathrm{Var}}\left( X \right) = n{K \over N}{(N-K) \over N}{N-n \over N-1}$$

Usage

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

variance( N, K, n )

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

var v = variance( 16, 11, 4 );
// returns ~0.688

v = variance( 2, 1, 1 );
// returns 0.25

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

var v = variance( NaN, 10, 4 );
// returns NaN

v = variance( 20, NaN, 4 );
// returns NaN

v = variance( 20, 10, 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 v = variance( 10.5, 5, 2 );
// returns NaN

v = variance( 10, 1.5, 2 );
// returns NaN

v = variance( 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 v = variance( 10, 5, 12 );
// returns NaN

v = variance( 10, 12, 5 );
// returns NaN

Examples

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

var v;
var i;
var N;
var K;
var n;

for ( i = 0; i < 10; i++ ) {
    N = round( randu() * 20 );
    K = round( randu() * N );
    n = round( randu() * K );
    v = variance( N, K, n );
    console.log( 'N: %d, K: %d, n: %d, Var(X;N,K,n): %d', N, K, n, v.toFixed( 4 ) );
}

---

C APIs

Usage

#include "stdlib/stats/base/dists/hypergeometric/variance.h"

stdlib_base_dists_hypergeometric_variance( N, K, n )

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

double out = stdlib_base_dists_hypergeometric_variance( 16, 11, 4 );
// returns ~0.688

The function accepts the following arguments:

• N: [in] double population size.
• K: [in] double subpopulation size.
• n: [in] double number of draws.

double stdlib_base_dists_hypergeometric_variance( const double N, const double K, const double n );

Examples

#include "stdlib/math/base/special/round.h"
#include "stdlib/stats/base/dists/hypergeometric/variance.h"
#include <stdio.h>
#include <stdlib.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v * ( max - min ) );
}

int main( void ) {
    double N;
    double K;
    double n;
    double v;
    int i;

    for ( i = 0; i < 10; i++ ) {
        N = stdlib_base_round( random_uniform( 0.0, 20.0 ) );
        K = stdlib_base_round( random_uniform( 0.0, N ) );
        n = stdlib_base_round( random_uniform( 0.0, K ) );
        v = stdlib_base_dists_hypergeometric_variance( N, K, n );
        printf( "N: %lf, K: %lf, n: %lf, Var(X;N,K,n): %lf\n", N, K, n, v );
    }
}