@stdlib/stats-base-dists-negative-binomial-pmf
v0.1.3TypeScript
Negative binomial distribution probability mass function (PMF).
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Probability Mass Function
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> [Negative binomial][negative-binomial-distribution] distribution [probability mass function][pmf] (PMF).
The [probability mass function][pmf] (PMF) for a [negative binomial][negative-binomial-distribution] random variable X is
where r > 0 is the number of successes until experiment is stopped and 0 < p <= 1 is the success probability. The random variable X denotes the number of failures until the r success is reached.
Installation
``bash`
npm install @stdlib/stats-base-dists-negative-binomial-pmf
Usage
`javascript`
var pmf = require( '@stdlib/stats-base-dists-negative-binomial-pmf' );
#### pmf( x, r, p )
Evaluates the [probability mass function][pmf] for a [negative binomial][negative-binomial-distribution] distribution with number of successes until experiment is stopped r and success probability p.
`javascript
var y = pmf( 5.0, 20.0, 0.8 );
// returns ~0.157
y = pmf( 21.0, 20.0, 0.5 );
// returns ~0.06
y = pmf( 5.0, 10.0, 0.4 );
// returns ~0.016
y = pmf( 0.0, 10.0, 0.9 );
// returns ~0.349
`
While r can be interpreted as the number of successes until the experiment is stopped, the [negative binomial][negative-binomial-distribution] distribution is also defined for non-integers r. In this case, r denotes shape parameter of the [gamma mixing distribution][negative-binomial-mixture-representation].
`javascript
var y = pmf( 21.0, 15.5, 0.5 );
// returns ~0.037
y = pmf( 5.0, 7.4, 0.4 );
// returns ~0.051
`
If provided a r which is not a positive number, the function returns NaN.
`javascript
var y = pmf( 2.0, 0.0, 0.5 );
// returns NaN
y = pmf( 2.0, -2.0, 0.5 );
// returns NaN
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pmf( NaN, 20.0, 0.5 );
// returns NaN
y = pmf( 0.0, NaN, 0.5 );
// returns NaN
y = pmf( 0.0, 20.0, NaN );
// returns NaN
`
If provided a success probability p outside of [0,1], the function returns NaN.
`javascript
var y = pmf( 2.0, 20, -1.0 );
// returns NaN
y = pmf( 2.0, 20, 1.5 );
// returns NaN
`
#### pmf.factory( r, p )
Returns a function for evaluating the [probability mass function][pmf] (PMF) of a [negative binomial][negative-binomial-distribution] distribution with number of successes until experiment is stopped r and success probability p.
`javascript
var mypmf = pmf.factory( 10, 0.5 );
var y = mypmf( 3.0 );
// returns ~0.03
y = mypmf( 10.0 );
// returns ~0.088
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var pmf = require( '@stdlib/stats-base-dists-negative-binomial-pmf' );
var opts = {
'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 30, opts );
var r = uniform( 10, 0.0, 50.0, opts );
var p = uniform( 10, 0.0, 1.0, opts );
logEachMap( 'x: %d, r: %0.4f, p: %0.4f, P(X=x;r,p): %0.4f', x, r, p, pmf );
`
*
Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-pmf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-pmf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-pmf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-pmf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-pmf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-pmf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-pmf/blob/main/branches.md
[negative-binomial-mixture-representation]: https://en.wikipedia.org/wiki/Negative_binomial_distribution#Gamma.E2.80.93Poisson_mixture
[negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution
[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function