Variance

Binomial distribution variance.

The variance for a binomial random variable is

where n is the number of trials and p is the success probability.

Usage

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

variance( n, p )

Returns the variance of a binomial distribution with number of trials n and success probability p.

var v = variance( 20, 0.1 );
// returns 1.8

v = variance( 50, 0.5 );
// returns 12.5

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

var v = variance( NaN, 0.5 );
// returns NaN

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

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

var v = variance( 1.5, 0.5 );
// returns NaN

v = variance( -2.0, 0.5 );
// returns NaN

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

var v = variance( 20, -1.0 );
// returns NaN

v = variance( 20, 1.5 );
// 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/binomial/variance' );

var v;
var i;
var n;
var p;

for ( i = 0; i < 10; i++ ) {
    n = round( randu() * 100.0 );
    p = randu();
    v = variance( n, p );
    console.log( 'n: %d, p: %d, Var(X;n,p): %d', n, p.toFixed( 4 ), v.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_binomial_variance( n, p )

Returns the variance of a binomial distribution with number of trials n and success probability p.

double out = stdlib_base_dists_binomial_variance( 100, 0.1 );
// returns 9.0

The function accepts the following arguments:

n: [in] int32_t number of trials.
p: [in] double success probability.

double stdlib_base_dists_binomial_variance( const int32_t n, const double p );

Examples

#include "stdlib/stats/base/dists/binomial/variance.h"
#include "stdlib/math/base/special/ceil.h"
#include <stdlib.h>
#include <stdint.h>
#include <stdio.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 ) {
    int32_t n;
    double p;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        n = stdlib_base_ceil( random_uniform( 0.0, 100.0 ) );
        p = random_uniform( 0.0, 1.0 );
        y = stdlib_base_dists_binomial_variance( n, p );
        printf( "n: %d, p: %lf, Var(X;n,p): %lf\n", n, p, y );
    }

    return 0;
}