Variance

Beta distribution variance.

The variance for a beta random variable is

where α > 0 is the first shape parameter and β > 0 is the second shape parameter.

Usage

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

variance( alpha, beta )

Returns the variance of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var v = variance( 1.0, 1.0 );
// returns ~0.083

v = variance( 4.0, 12.0 );
// returns ~0.011

v = variance( 8.0, 2.0 );
// returns ~0.015

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 alpha <= 0, the function returns NaN.

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

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

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

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

v = variance( 1.0, -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/beta/variance' );

var alpha;
var beta;
var v;
var i;

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

C APIs

Usage

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

stdlib_base_dists_beta_variance( alpha, beta )

Returns the variance of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

double out = stdlib_base_dists_beta_variance( 1.0, 1.0 );
// returns ~0.083

The function accepts the following arguments:

alpha: [in] double first shape parameter.
beta: [in] double second shape parameter.

double stdlib_base_dists_beta_variance( const double alpha, const double beta );

Examples

#include "stdlib/stats/base/dists/beta/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 alpha;
    double beta;
    double y;
    int i;
    for ( i = 0; i < 25; i++ ) {
        alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        beta = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        y = stdlib_base_dists_beta_variance( alpha, beta );
        printf( "α: %lf, β: %lf, Var(X;α,β): %lf\n", alpha, beta, y );
    }
}