Variance

Negative binomial distribution variance.

The variance for a negative binomial random variable is

where r is the number of successes until experiment is stopped and p is the success probability in each trial. The random variable X denotes the number of failures until the r success is reached.

Installation

npm install @stdlib/stats-base-dists-negative-binomial-variance

Usage

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

variance( r, p )

Returns the variance of a negative binomial distribution with parameters r (number of successes until experiment is stopped) and p (success probability).

var v = variance( 100, 0.2 );
// returns ~2000.0

v = variance( 50, 0.5 );
// returns 100.0

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

var v = variance( NaN, 0.5 );
// returns NaN

v = variance( 20, NaN );
// returns NaN

If provided a r which is not a positive number, the function returns NaN.

var v = variance( -2.0, 0.5 );
// returns NaN

If provided a success probability p outside of [0,1], the function returns NaN.

var v = variance( 20, -1.0 );
// returns NaN

v = variance( 20, 1.5 );
// 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-negative-binomial-variance' );

var opts = {
    'dtype': 'float64'
};
var r = uniform( 10, 0.0, 100.0, opts );
var p = uniform( 10, 0.0, 1.0, opts );

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

C APIs

Usage

#include "stdlib/stats/base/dists/negative-binomial/variance.h"

stdlib_base_dists_negative_binomial_variance( r, p )

Returns the variance of a negative binomial distribution with parameters r (number of successes until experiment is stopped) and p (success probability).

double v = stdlib_base_dists_negative_binomial_variance( 100.0, 0.2 );
// returns ~2000.0

The function accepts the following arguments:

• r: [in] double number of successes until experiment is stopped.
• p: [in] double success probability.

double stdlib_base_dists_negative_binomial_variance( const double r, const double p );

Examples

#include "stdlib/stats/base/dists/negative-binomial/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 r;
    double p;
    double v;
    int i;


    for ( i = 0; i < 10; i++ ) {
        r = random_uniform( -1.0, 100.0 );
        p = random_uniform( 0.0, 1.0 );
        v = stdlib_base_dists_negative_binomial_variance( r, p );
        printf( "r: %.4f, p: %.4f, Var(X;r,p): %.4f\n", r, p, v );
    }
}

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.