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.

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 );
    }
}