Variance

Discrete uniform distribution variance.

The variance for a discrete uniform random variable is

where a is the minimum support and b the maximum support of the distribution.

Installation

npm install @stdlib/stats-base-dists-discrete-uniform-variance

Usage

var variance = require( '@stdlib/stats-base-dists-discrete-uniform-variance' );

variance( a, b )

Returns the variance of a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var v = variance( 0, 1 );
// returns ~0.25

v = variance( 4, 12 );
// returns ~6.667

v = variance( -4, 4 );
// returns ~6.667

If a or b is not an integer value, the function returns NaN.

var v = variance( 0.1, 2 );
// returns NaN

v = variance( 0, 2.2 );
// returns NaN

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

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

If provided a > b, the function returns NaN.

var v = variance( 3, 2 );
// returns NaN

v = variance( -1, -2 );
// returns NaN

Examples

var randint = require( '@stdlib/random-base-discrete-uniform' );
var variance = require( '@stdlib/stats-base-dists-discrete-uniform-variance' );

var randa = randint.factory( 0, 10 );
var randb = randint.factory();
var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = randa();
    b = randb( a, a+randa() );
    v = variance( a, b );
    console.log( 'a: %d, b: %d, Var(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}

C APIs

Usage

#include "stdlib/stats/base/dists/discrete-uniform/variance.h"

stdlib_base_dists_discrete_uniform_variance( a, b )

Returns the variance of a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

double out = stdlib_base_dists_discrete_uniform_variance( 0, 1 );
// returns ~0.25

The function accepts the following arguments:

• a: [in] int32_t minimum support.
• b: [in] int32_t maximum support.

double stdlib_base_dists_discrete_uniform_variance( const int32_t a, const int32_t b );

Examples

#include "stdlib/stats/base/dists/discrete-uniform/variance.h"
#include "stdlib/math/base/special/round.h"
#include <stdint.h>
#include <stdlib.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 a;
    int32_t b;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        a = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
        b = stdlib_base_round( random_uniform( 0.0, 10.0 ) ) + a;
        y = stdlib_base_dists_discrete_uniform_variance( a, b );
        printf( "a: %d, b: %d, Var(X;a,b): %lf\n", a, b, y );
    }
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.