Negative Binomial

Negative binomial distribution constructor.

Installation

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

Usage

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

NegativeBinomial( [r, p] )

Returns a negative binomial distribution object.

var nbinomial = new NegativeBinomial();

var mu = nbinomial.mean;
// returns 1.0

By default, r = 1.0 and p = 0.5. To create a distribution having a different r (number of trials until experiment is stopped) and p (success probability), provide the corresponding arguments.

var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var mu = nbinomial.mean;
// returns 16.0

nbinomial

A negative binomial distribution object has the following properties and methods...

Writable Properties

nbinomial.r

Number of trials of the distribution. r must be a positive number.

var nbinomial = new NegativeBinomial();

var r = nbinomial.r;
// returns 1.0

nbinomial.r = 4.5;

r = nbinomial.r;
// returns 4.5

nbinomial.p

Success probability of the distribution. p must be a number between 0 and 1.

var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var p = nbinomial.p;
// returns 0.2

nbinomial.p = 0.7;

p = nbinomial.p;
// returns 0.7

Computed Properties

NegativeBinomial.prototype.kurtosis

Returns the excess kurtosis.

var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var kurtosis = nbinomial.kurtosis;
// returns ~0.522

NegativeBinomial.prototype.mean

Returns the expected value.

var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var mu = nbinomial.mean;
// returns ~18.0

NegativeBinomial.prototype.mode

Returns the mode.

var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var mode = nbinomial.mode;
// returns 16.0

NegativeBinomial.prototype.skewness

Returns the skewness.

var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var skewness = nbinomial.skewness;
// returns ~0.596

NegativeBinomial.prototype.stdev

Returns the standard deviation.

var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var s = nbinomial.stdev;
// returns ~6.708

NegativeBinomial.prototype.variance

Returns the variance.

var nbinomial = new NegativeBinomial( 12.0, 0.4 );

var s2 = nbinomial.variance;
// returns ~45.0

Methods

NegativeBinomial.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var y = nbinomial.cdf( 3.5 );
// returns ~0.033

NegativeBinomial.prototype.logpmf( x )

Evaluates the natural logarithm of the probability mass function (PMF).

var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var y = nbinomial.logpmf( 4.0 );
// returns ~-3.775

NegativeBinomial.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var y = nbinomial.mgf( 0.1 );
// returns ~1.66

NegativeBinomial.prototype.pmf( x )

Evaluates the probability mass function (PMF).

var nbinomial = new NegativeBinomial( 4.0, 0.2 );

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

NegativeBinomial.prototype.quantile( p )

Evaluates the quantile function at probability p.

var nbinomial = new NegativeBinomial( 4.0, 0.2 );

var y = nbinomial.quantile( 0.5 );
// returns 15.0

y = nbinomial.quantile( 1.9 );
// returns NaN

Examples

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

var nbinomial = new NegativeBinomial( 10.0, 0.4 );

var mu = nbinomial.mean;
// returns 15.0

var mode = nbinomial.mode;
// returns 13.0

var s2 = nbinomial.variance;
// returns ~37.5

var y = nbinomial.cdf( 8.0 );
// returns ~0.135

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 © 2016-2024. The Stdlib Authors.