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

upper F left-parenthesis x minus 1 semicolon upper N comma upper K comma n right-parenthesis less-than p less-than-or-equal-to upper F left-parenthesis x semicolon upper N comma upper K comma n right-parenthesis

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.

Usage

var quantile = require( '@stdlib/math/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 exceeds population size N, the function returns NaN.

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

y = cdf( 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 = 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/math/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 ) );
}