Skip to content

Latest commit

 

History

History
351 lines (225 loc) · 14.2 KB

README.md

File metadata and controls

351 lines (225 loc) · 14.2 KB
Raw
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!

Gamma

NPM version Build Status Coverage Status

Gamma distribution.

Installation

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

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

gamma

Gamma distribution.

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

The namespace contains the following distribution functions:

The namespace contains the following functions for calculating distribution properties:

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

var Gamma = require( '@stdlib/stats-base-dists-gamma' ).Gamma;

var dist = new Gamma( 2.0, 4.0 );

var y = dist.cdf( 0.5 );
// returns ~0.594

Examples

var gammaRandomFactory = require( '@stdlib/random-base-gamma' ).factory;
var filledarrayby = require( '@stdlib/array-filled-by' );
var Float64Array = require( '@stdlib/array-float64' );
var variance = require( '@stdlib/stats-base-variance' );
var linspace = require( '@stdlib/array-base-linspace' );
var mean = require( '@stdlib/stats-base-mean' );
var abs = require( '@stdlib/math-base-special-abs' );
var gamma = require( '@stdlib/stats-base-dists-gamma' );

// Define the shape and scale parameters:
var alpha = 3.0; // shape parameter (α)
var beta = 2.0;  // scale parameter (β)

// Generate an array of x values:
var x = linspace( 0.0, 20.0, 100 );

// Compute the PDF for each x:
var gammaPDF = gamma.pdf.factory( alpha, beta );
var pdf = filledarrayby( x.length, 'float64', gammaPDF );

// Compute the CDF for each x:
var gammaCDF = gamma.cdf.factory( alpha, beta );
var cdf = filledarrayby( x.length, 'float64', gammaCDF );

// Output the PDF and CDF values:
console.log( 'x values: %s', x );
console.log( 'PDF values: %s', pdf );
console.log( 'CDF values: %s', cdf );

// Compute statistical properties:
var theoreticalMean = gamma.mean( alpha, beta );
var theoreticalVariance = gamma.variance( alpha, beta );
var theoreticalSkewness = gamma.skewness( alpha, beta );
var theoreticalKurtosis = gamma.kurtosis( alpha, beta );

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

// Generate random samples from the gamma distribution:
var rgamma = gammaRandomFactory( alpha, beta );
var n = 300;
var samples = filledarrayby( n, 'float64', rgamma );

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

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

// Compare sample statistics to theoretical values:
console.log( 'Difference in Mean: %s', abs( theoreticalMean - sampleMean ) );
console.log( 'Difference in Variance: %s', abs( theoreticalVariance - sampleVariance ) );

// Demonstrate that the sum of `k` gamma variables is a gamma-distributed sum of `k` gamma(α, β) variables with same β is `gamma(k*α, β)`:
var k = 5;
var sumSamples = new Float64Array( n );

var sum;
var i;
var j;
for ( i = 0; i < sumSamples.length; i++ ) {
    sum = 0.0;
    for ( j = 0; j < k; j++ ) {
        sum += rgamma();
    }
    sumSamples[ i ] = sum;
}

// Theoretical parameters for the sum:
var sumAlpha = k * alpha;
var sumMean = gamma.mean( sumAlpha, beta );
var sumVariance = gamma.variance( sumAlpha, beta );

console.log( 'Sum Theoretical Mean: %s', sumMean );
console.log( 'Sum Theoretical Variance: %s', sumVariance );

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

console.log( 'Sum Sample Mean: %s', sumSampleMean );
console.log( 'Sum Sample Variance: %s', 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

Chat

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.