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Negative Binomial

Negative binomial distribution.

Installation

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

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

negativeBinomial

Negative binomial distribution.

var dist = negativeBinomial;
// returns {...}

The namespace contains the following distribution functions:

• cdf( x, r, p ): negative binomial distribution cumulative distribution function.
• logpmf( x, r, p ): evaluate the natural logarithm of the probability mass function (PMF) for a negative binomial distribution.
• mgf( t, r, p ): negative binomial distribution moment-generating function (MGF).
• pmf( x, r, p ): negative binomial distribution probability mass function (PMF).
• quantile( k, r, p ): negative binomial distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

• kurtosis( r, p ): negative binomial distribution excess kurtosis.
• mean( r, p ): negative binomial distribution expected value.
• mode( r, p ): negative binomial distribution mode.
• skewness( r, p ): negative binomial distribution skewness.
• stdev( r, p ): negative binomial distribution standard deviation.
• variance( r, p ): negative binomial distribution variance.

The namespace contains a constructor function for creating a negative binomial distribution object.

• NegativeBinomial( [r, p] ): negative binomial distribution constructor.

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

var dist = new NegativeBinomial( 4.0, 0.2 );

var y = dist.pmf( 4.0 );
// returns ~0.023

Examples

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

/*
* Let's take an example of flipping a biased coin until getting 5 heads.
* This situation can be modeled using a Negative Binomial distribution with r = 5 and p = 1/2.
*/

var r = 5.0;
var p = 1/2;

// Mean can be used to calculate the average number of trials needed to get 5 heads:
console.log( negativeBinomial.mean( r, p ) );
// => 5

// PMF can be used to calculate the probability of getting heads on a specific trial (say on the 8th trial):
console.log( negativeBinomial.pmf( 8, r, p ) );
// => ~0.06

// CDF can be used to calculate the probability up to a certain number of trials (say up to 8 trials):
console.log( negativeBinomial.cdf( 8, r, p ) );
// => ~0.867

// Quantile can be used to calculate the number of trials at which you can be 80% confident that the actual number will not exceed:
console.log( negativeBinomial.quantile( 0.8, r, p ) );
// => 7

// Standard deviation can be used to calculate the measure of the spread of trials around the mean:
console.log( negativeBinomial.stdev( r, p ) );
// => ~3.162

// Skewness can be used to calculate the asymmetry of the distribution of trials:
console.log( negativeBinomial.skewness( r, p ) );
// => ~0.949

// MGF can be used for more advanced statistical analyses and generating moments of the distribution:
console.log( negativeBinomial.mgf( 0.5, r, p ) );
// => ~2277.597

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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.

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