Variance

Triangular distribution variance.

The variance for a triangular random variable is

where a is the lower limit, b is the upper limit and c is the mode.

Installation

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

Usage

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

variance( a, b, c )

Returns the variance of a triangular distribution with minimum support a, maximum support b, and mode c.

var v = variance( 0.0, 1.0, 0.8 );
// returns ~0.047

v = variance( 4.0, 12.0, 5.0 );
// returns ~3.167

v = variance( 2.0, 8.0, 5.0 );
// returns 1.5

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

var v = variance( NaN, 4.0, 2.0 );
// returns NaN

v = variance( 0.0, NaN, 2.0 );
// returns NaN

v = variance( 0.0, 4.0, NaN );
// returns NaN

If provided parameters not satisfying a <= c <= b, the function returns NaN.

var y = variance( 1.0, 0.0, 1.5 );
// returns NaN

y = variance( 0.0, 1.0, -1.0 );
// returns NaN

y = variance( 0.0, -1.0, 0.5 );
// returns NaN

Examples

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

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

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

C APIs

Usage

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

stdlib_base_dists_triangular_variance( a, b, c )

Returns the variance of a triangular distribution with minimum support a, maximum support b, and mode c.

double out = stdlib_base_dists_triangular_variance( 0.0, 1.0, 0.5 );
// returns ~0.056

The function accepts the following arguments:

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

double stdlib_base_dists_triangular_variance( const double a, const double b, const double c );

Examples

#include "stdlib/stats/base/dists/triangular/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 c;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        a = random_uniform( 0.0, 10.0 );
        b = random_uniform( a, a+10.0 );
        c = random_uniform( a, b );
        y = stdlib_base_dists_triangular_variance( a, b, c );
        printf( "a: %lf, b: %lf, c: %lf, Var(X;a,b,c): %lf\n", a, b, c, 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.