About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Quantile Function

Negative binomial distribution quantile function.

The quantile function for a negative binomial random variable X returns for any k satisfying 0 <= k <= 1 the value x for which

$$F(x-1;r,p) < k \le F(x;r,p)$$

holds, where F is the cumulative distribution function (CDF) of a negative binomial distribution with parameters r and p, where r is the number of successes until the experiment is stopped and p is the success probability. The random variable X denotes the number of failures until the r success is reached.

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

quantile( k, r, p )

Evaluates the quantile function for a negative binomial distribution with number of successes until experiment is stopped r and success probability p.

var y = quantile( 0.9, 20.0, 0.2 );
// returns 106

y = quantile( 0.9, 20.0, 0.8 );
// returns 8

y = quantile( 0.5, 10.0, 0.4 );
// returns 14

y = quantile( 0.0, 10.0, 0.9 );
// returns 0

If provided an input value k outside of [0,1], the function returns NaN.

var y = quantile( 1.1, 20.0, 0.5 );
// returns NaN

y = quantile( -0.1, 20.0, 0.5 );
// returns NaN

While r can be interpreted as the number of successes until the experiment is stopped, the negative binomial distribution is also defined for non-integers r. In this case, r denotes shape parameter of the gamma mixing distribution.

var y = quantile( 0.5, 15.5, 0.5 );
// returns 15

y = quantile( 0.3, 7.4, 0.4 );
// returns 8

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

var y = quantile( 0.5, 0.0, 0.5 );
// returns NaN

y = quantile( 0.5, -2.0, 0.5 );
// returns NaN

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

var y = quantile( NaN, 20.0, 0.5 );
// returns NaN

y = quantile( 0.3, NaN, 0.5 );
// returns NaN

y = quantile( 0.3, 20.0, NaN );
// returns NaN

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

var y = quantile( 0.3, 20.0, -1.0 );
// returns NaN

y = quantile( 0.3, 20.0, 1.5 );
// returns NaN

quantile.factory( r, p )

Returns a function for evaluating the quantile function for a negative binomial distribution with number of successes until experiment is stopped r and success probability p.

var myquantile = quantile.factory( 10.0, 0.5 );
var y = myquantile( 0.1 );
// returns 5

y = myquantile( 0.9 );
// returns 16

Examples

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

var i;
var k;
var r;
var p;
var y;

for ( i = 0; i < 10; i++ ) {
    k = randu();
    r = randu() * 100;
    p = randu();
    y = quantile( k, r, p );
    console.log( 'k: %d, r: %d, p: %d, Q(k;r,p): %d', k.toFixed( 4 ), r.toFixed( 4 ), p.toFixed( 4 ), 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

---

Copyright

Copyright © 2016-2024. The Stdlib Authors.