Variance

Arcsine distribution variance.

The variance for an arcsine random variable with minimum support a and maximum support b is

Installation

npm install @stdlib/stats-base-dists-arcsine-variance

Usage

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

variance( a, b )

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

var v = variance( 0.0, 1.0 );
// returns ~0.125

v = variance( 4.0, 12.0 );
// returns 8.0

v = variance( 2.0, 8.0 );
// returns ~4.5

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

var v = variance( NaN, 2.0 );
// returns NaN

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

If provided a >= b, the function returns NaN.

var v = variance( 3.0, 2.0 );
// returns NaN

v = variance( 3.0, 3.0 );
// returns NaN

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var variance = require( '@stdlib/stats-base-dists-arcsine-variance' );

var opts = {
    'dtype': 'float64'
};
var a = uniform( 25, 0.0, 10.0, opts );
var b = uniform( a.length, 10.0, 20.0, opts );

logEachMap( 'a: %0.4f, b: %0.4f, Var(X;a,b): %0.4f', a, b, variance );

C APIs

Usage

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

stdlib_base_dists_arcsine_variance( a, b )

Returns the variance of an arcsine distribution.

double out = stdlib_base_dists_arcsine_variance( 0.0, 1.0 );
// returns ~0.125

The function accepts the following arguments:

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

double stdlib_base_dists_arcsine_variance( const double a, const double b );

Examples

#include "stdlib/stats/base/dists/arcsine/variance.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 ) {
    double a;
    double b;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        a = random_uniform( 0.0, 10.0 );
        b = random_uniform( a, a+10.0 );
        y = stdlib_base_dists_arcsine_variance( a, b );
        printf( "a: %lf, b: %lf, 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.