Geometric

Geometric distribution.

Installation

npm install @stdlib/stats-base-dists-geometric

Usage

var geometric = require( '@stdlib/stats-base-dists-geometric' );

geometric

Geometric distribution.

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

The namespace contains the following distribution functions:

• cdf( x, p ): geometric distribution cumulative distribution function.
• logcdf( x, p ): geometric distribution logarithm of cumulative distribution function.
• logpmf( x, p ): geometric distribution logarithm of probability mass function (PMF).
• mgf( t, p ): geometric distribution moment-generating function (MGF).
• pmf( x, p ): geometric distribution probability mass function (PMF).
• quantile( r, p ): geometric distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

• entropy( p ): geometric distribution entropy.
• kurtosis( p ): geometric distribution excess kurtosis.
• mean( p ): geometric distribution expected value.
• median( p ): geometric distribution median.
• mode( p ): geometric distribution mode.
• skewness( p ): geometric distribution skewness.
• stdev( p ): geometric distribution standard deviation.
• variance( p ): geometric distribution variance.

The namespace contains a constructor function for creating a geometric distribution object.

• Geometric( [p] ): geometric distribution constructor.

var Geometric = require( '@stdlib/stats-base-dists-geometric' ).Geometric;

var dist = new Geometric( 0.2 );

var y = dist.logpmf( 3.0 );
// returns ~-2.279

y = dist.logpmf( 2.3 );
// returns -Infinity

Examples

var geometricRandomFactory = require( '@stdlib/random-base-geometric' ).factory;
var negativeBinomial = require( '@stdlib/stats-base-dists-negative-binomial' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var variance = require( '@stdlib/stats-strided-variance' );
var linspace = require( '@stdlib/array-base-linspace' );
var mean = require( '@stdlib/stats-strided-mean' );
var abs = require( '@stdlib/math-base-special-abs' );
var geometric = require( '@stdlib/stats-base-dists-geometric' );

// Define the success probability:
var p = 0.3; // Probability of success on each trial

// Generate an array of x values (number of failures before first success):
var x = linspace( 0, 10, 11 ); // Geometric distribution is discrete

// Compute the PMF for each x:
var geometricPMF = geometric.pmf.factory( p );
var pmf = filledarrayBy( x.length, 'float64', geometricPMF );

// Compute the CDF for each x:
var geometricCDF = geometric.cdf.factory( p );
var cdf = filledarrayBy( x.length, 'float64', geometricCDF );

// Output the PMF and CDF values:
console.log( 'x values: ', x );
console.log( 'PMF values: ', pmf );
console.log( 'CDF values: ', cdf );

// Compute statistical properties:
var theoreticalMean = geometric.mean( p );
var theoreticalVariance = geometric.variance( p );
var theoreticalSkewness = geometric.skewness( p );
var theoreticalKurtosis = geometric.kurtosis( p );

console.log( 'Theoretical Mean: ', theoreticalMean );
console.log( 'Theoretical Variance: ', theoreticalVariance );
console.log( 'Skewness: ', theoreticalSkewness );
console.log( 'Kurtosis: ', theoreticalKurtosis );

// Generate random samples from the geometric distribution:
var rgeom = geometricRandomFactory( p );
var n = 1000;
var samples = filledarrayBy( n, 'float64', rgeom );

// Compute sample mean and variance:
var sampleMean = mean( n, samples, 1 );
var sampleVariance = variance( n, 1, samples, 1 );

console.log( 'Sample Mean: ', sampleMean );
console.log( 'Sample Variance: ', sampleVariance );

// Demonstrate the memoryless property:
var s = 2.0;
var t = 3.0;
var prob1 = ( 1.0 - geometric.cdf( s + t - 1.0, p ) ) /
    ( 1.0 - geometric.cdf( s - 1.0, p ) );
var prob2 = 1.0 - geometric.cdf( t - 1.0, p );

console.log( 'P(X > s + t | X > s): ', prob1 );
console.log( 'P(X > t): ', prob2 );
console.log( 'Difference: ', abs( prob1 - prob2 ) );

// Demonstrate that the sum of k independent geometric random variables follows a negative binomial distribution:
var k = 5;
function drawSum() {
    var sum = 0;
    var j;
    for ( j = 0; j < k; j++ ) {
        sum += rgeom();
    }
    return sum;
}
var sumSamples = filledarrayBy( n, 'float64', drawSum );

// Compute sample mean and variance for the sum:
var sumSampleMean = mean( n, sumSamples, 1 );
var sumSampleVariance = variance( n, 1, sumSamples, 1 );

// Theoretical mean and variance of Negative Binomial distribution:
var nbMean = negativeBinomial.mean( k, p );
var nbVariance = negativeBinomial.variance( k, p );

console.log( 'Sum Sample Mean: ', sumSampleMean );
console.log( 'Sum Sample Variance: ', sumSampleVariance );
console.log( 'Negative Binomial Mean: ', nbMean );
console.log( 'Negative Binomial Variance: ', nbVariance );

// Compare sample statistics to theoretical values:
console.log( 'Difference in Mean: ', abs( nbMean - sumSampleMean ) );
console.log( 'Difference in Variance: ', abs( nbVariance - sumSampleVariance ) );

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.