Variance

Student's t distribution variance.

The variance for a Student's t random variable with degrees of freedom ν is

For ν smaller than one, the variance is not defined.

Installation

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

Usage

var variance = require( '@stdlib/stats-base-dists-t-variance' );

variance( v )

Returns the variance of a Student's t distribution with degrees of freedom v.

var y = variance( 9.0 );
// returns ~1.286

y = variance( 3.5 );
// returns ~2.333

If provided 1 < v <= 2, the function returns infinity.

var y = variance( 1.5 );
// returns Infinity

y = variance( 2.0 );
// returns Infinity

If provided v <= 1, the function returns NaN.

var y = variance( -1.0 );
// returns NaN

y = variance( 0.8 );
// returns NaN

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var variance = require( '@stdlib/stats-base-dists-t-variance' );

var opts = {
    'dtype': 'float64'
};
var v = uniform( 10, 0.0, 20.0, opts );

logEachMap( 'v: %0.4f, Var(X;v): %0.4f', v, variance );

C APIs

Usage

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

stdlib_base_dists_t_variance( v )

Returns the variance for a Student's t-distribution.

double out = stdlib_base_dists_t_variance( 5.0 );
// returns ~1.667

The function accepts the following arguments:

• v: [in] double degrees of freedom.

double stdlib_base_dists_t_variance( const double v );

Examples

#include "stdlib/stats/base/dists/t/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 v;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        v = random_uniform( 2.1, 100.0 );
        y = stdlib_base_dists_t_variance( v );
        printf( "v: %.4f, Var(X;v): %.4f\n", v, 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.