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Variance

F distribution variance.

The variance for a F random variable is

$$\mathop{\mathrm{Var}}\left( X \right) = \frac{2\,d_{2}^{2}\,(d_{1}+d_{2}-2)}{d_{1}(d_{2}-2)^{2}(d_{2}-4)}$$

for d1 > 0 and d2 > 4. Otherwise, the variance is not defined.

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

variance( d1, d2 )

Returns the variance of an F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

var v = variance( 4.0, 5.0 );
// returns ~9.722

v = variance( 4.0, 12.0 );
// returns ~1.26

v = variance( 8.0, 5.0 );
// returns ~7.639

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

var v = variance( NaN, 5.0 );
// returns NaN

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

If provided d1 <= 0, the function returns NaN.

var v = variance( 0.0, 5.0 );
// returns NaN

v = variance( -1.0, 5.0 );
// returns NaN

If provided d2 <= 4, the function returns NaN.

var v = variance( 3.0, 4.0 );
// returns NaN

v = variance( 3.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var variance = require( '@stdlib/stats-base-dists-f-variance' );

var d1;
var d2;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    d1 = ( randu()*10.0 ) + EPS;
    d2 = ( randu()*20.0 ) + EPS;
    v = variance( d1, d2 );
    console.log( 'd1: %d, d2: %d, Var(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) );
}

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C APIs

Usage

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

stdlib_base_dists_f_variance( d1, d2 )

Evaluates the variance of an F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

double out = stdlib_base_dists_f_variance( 3.0, 5.0 );
// returns ~11.111

The function accepts the following arguments:

• d1: [in] double numerator degrees of freedom.
• d2: [in] double denominator degrees of freedom.

double stdlib_base_dists_f_variance( const double d1, const double d2 );

Examples

#include "stdlib/stats/base/dists/f/variance.h"
#include "stdlib/constants/float64/eps.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 d1;
    double d2;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        d1 = random_uniform( 0.0, 10.0 ) + STDLIB_CONSTANT_FLOAT64_EPS;
        d2 = random_uniform( 0.0, 20.0 ) + STDLIB_CONSTANT_FLOAT64_EPS;
        y = stdlib_base_dists_f_variance( d1, d2 );
        printf( "d1: %lf, d2: %lf, Var(X;d1,d2): %lf\n", d1, d2, y );
    }
}

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.