Variance

Arcsine distribution variance.

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

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

var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = ( randu()*10.0 );
    b = ( randu()*10.0 ) + a;
    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/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 );
    }
}