Quantile Function

Binomial distribution quantile function.

The quantile function for a binomial random variable returns, for any r satisfying 0 <= r <= 1, the value x for which the relation

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

holds, where F is the cumulative distribution function (CDF) of a binomial random variable, n is the number of trials, and 0 <= p <= 1 is the success probability.

Usage

var quantile = require( '@stdlib/math/base/dists/binomial/quantile' );

quantile( r, n, p )

Evaluates the quantile function for a binomial distribution with number of trials n and success probability p at value r.

var y = quantile( 0.4, 20, 0.2 );
// returns 2

y = quantile( 0.8, 20, 0.2 );
// returns 5

y = quantile( 0.5, 10, 0.4 );
// returns 4

y = quantile( 0.0, 10, 0.4 );
// returns 0

y = quantile( 1.0, 10, 0.4 );
// returns 10

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

var y = quantile( NaN, 20, 0.5 );
// returns NaN

y = quantile( 0.2, NaN, 0.5 );
// returns NaN

y = quantile( 0.2, 20, NaN );
// returns NaN

If provided a number of trials n which is not a nonnegative integer, the function returns NaN.

var y = quantile( 0.5, 1.5, 0.5 );
// returns NaN

y = quantile( 0.5, -2.0, 0.5 );
// returns NaN

If provided a success probability p outside of [0,1], the function returns NaN.

var y = quantile( 0.5, 20, -1.0 );
// returns NaN

y = quantile( 0.5, 20, 1.5 );
// returns NaN

quantile.factory( n, p )

Returns a function for evaluating the quantile function of a binomial distribution with number of trials n and success probability p.

var myquantile = quantile.factory( 10, 0.5 );

var y = myquantile( 0.1 );
// returns 3

y = myquantile( 0.9 );
// returns 7

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var quantile = require( '@stdlib/math/base/dists/binomial/quantile' );

var r;
var i;
var n;
var p;
var y;

for ( i = 0; i < 10; i++ ) {
    r = randu();
    n = round( randu() * 100.0 );
    p = randu();
    y = quantile( r, n, p );
    console.log( 'r: %d, n: %d, p: %d, Q(r;n,p): %d', r.toFixed( 4 ), n, p.toFixed( 4 ) );
}