Standard Deviation

Kumaraswamy's double bounded distribution standard deviation.

The standard deviation for a Kumaraswamy's double bounded random variable with first shape parameter a and second shape parameter b is

where the raw moments of the distribution are given by

with B denoting the beta function.

Installation

npm install @stdlib/stats-base-dists-kumaraswamy-stdev

Usage

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

stdev( a, b )

Returns the standard deviation of a Kumaraswamy's double bounded distribution with first shape parameter a and second shape parameter b.

var v = stdev( 1.0, 1.0 );
// returns ~0.289

v = stdev( 4.0, 12.0 );
// returns ~0.13

v = stdev( 2.0, 8.0 );
// returns ~0.146

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 <= 0, the function returns NaN.

var y = stdev( -1.0, 0.5 );
// returns NaN

y = stdev( 0.0, 0.5 );
// returns NaN

If provided b <= 0, the function returns NaN.

var y = stdev( 0.5, -1.0 );
// returns NaN

y = stdev( 0.5, 0.0 );
// returns NaN

Examples

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

var opts = {
    'dtype': 'float64'
};
var a = uniform( 10, 0.0, 10.0, opts );
var b = uniform( 10, 0.0, 10.0, opts );

logEachMap( 'a: %0.4f, b: %0.4f, SD(X;a,b): %0.4f', a, b, stdev );

C APIs

Usage

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

stdlib_base_dists_kumaraswamy_stdev( a, b )

Returns the standard deviation of a Kumaraswamy's double bounded distribution with first shape parameter a and second shape parameter b.

double v = stdlib_base_dists_kumaraswamy_stdev( 0.5, 1.0 );
// returns ~0.298

The function accepts the following arguments:

• a: [in] double first shape parameter.
• b: [in] double second shape parameter.

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

Examples

#include "stdlib/stats/base/dists/kumaraswamy/stdev.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( 0.1, 20.0 );
        b = random_uniform( 0.1, 20.0 );
        y = stdlib_base_dists_kumaraswamy_stdev( a, b );
        printf( "a: %lf, b: %lf, SD(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.