README.md

Standard Deviation

Arcsine distribution standard deviation.

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

$$\sigma = {\tfrac{1}{\sqrt{8}}}(b-a)$$

Usage

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

stdev( a, b )

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

var v = stdev( 0.0, 1.0 );
// returns ~0.354

v = stdev( 4.0, 12.0 );
// returns ~2.828

v = stdev( 2.0, 8.0 );
// returns ~2.121

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

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

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

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

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

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

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    a = ( randu()*10.0 );
    b = ( randu()*10.0 ) + a;
    v = stdev( a, b );
    console.log( 'a: %d, b: %d, SD(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}

---

C APIs

Usage

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

stdlib_base_dists_arcsine_stdev( a, b )

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

double out = stdlib_base_dists_arcsine_stdev( 4.0, 12.0 );
// returns ~2.828

The function accepts the following arguments:

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

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

Examples

#include "stdlib/stats/base/dists/arcsine/stdev.h"
#include <stdio.h>
#include <stdlib.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 s;
    int i;

    for ( i = 0; i < 10; i++ ) {
        a = random_uniform( 0.0, 10.0 );
        b = random_uniform( a, a + 10.0 );
        s = stdlib_base_dists_arcsine_stdev( a, b );
        printf( "a: %lf, b: %lf, SD(X;a,b): %lf\n", a, b, s );
    }
}