Gamma Random Variables

Creates a matrix or array filled with draws from a gamma distribution.

Installation

$ npm install distributions-gamma-random

For use in the browser, use browserify.

Usage

var random = require( 'distributions-gamma-random' );

random( [dims][, opts] )

Creates a matrix or array filled with draws from a gamma distribution. The dims argument may either be a positive integer specifying a length or an array of positive integers specifying dimensions. If no dims argument is supplied,the function returns a single random draw from a gamma distribution.

var out;

// Set seed
random.seed = 2;

out = random( 5 );
// returns [ ~0.192, ~0.319, ~0.714, ~0.861, ~0.974 ]

out = random( [2,1,2] );
// returns [ [ [~0.0375,~0.6443] ], [ [~0.5867,~0.980] ] ]

The function accepts the following options:

• alpha: shape parameter. Default: 1.
• beta: rate parameter. Default: 1.
• seed: positive integer used as a seed to initialize the generator. If not supplied, uniformly distributed random numbers are generated via an underlying generator seedable by setting the seed property of the exported function.
• dtype: output data type (see matrix for a list of acceptable data types). Default: generic.

The gamma distribution is a function of two parameters: alpha > 0(shape parameter) and beta > 0(rate parameter). By default, alpha is equal to 1 and beta is equal to 1. To adjust either parameter, set the corresponding option.

var out = random( 5, {
	'alpha': 30,
	'beta': 5,
});
// returns [ ~5.861, ~4.767, ~7.006, ~6.287, ~6.737 ]

To be able to reproduce the generated random numbers, set the seed option to a positive integer.

var out = random( 3, {
	'seed': 22
});
// returns [ ~0.267, ~1.047, ~0.203 ]

var out = random( 3, {
    'seed': 22
});
// returns [ ~0.267, ~1.047, ~0.203 ]

If no seed option is supplied, each function call uses a common underlying uniform number generator. A positive-integer seed for this underlying generator can be supplied by setting the seed property of the exported function.

random.seed = 11;
var out = random();
// returns ~0.162

var out = random();
// returns ~0.606

random.seed = 11;
var out = random();
// returns ~0.162

var out = random();
// returns ~0.606

By default, the output data structure is a generic array. To output a typed array or matrix, set the dtype option.

var out;

out = random( 5, {
	'dtype': 'float32'
});
// returns Float32Array( [~2.131,~2.051,~1.701,1.54,~1.111] )

out = random( [3,2], {
	'dtype': 'float64'
});
/*
	[ ~0.786 ~1.724
	  ~1.664 ~0.652
	  ~1.042 ~0.231 ]
*/

Notes:

• Currently, for more than 2 dimensions, the function outputs a generic array and ignores any specified dtype.

  var out = random( [2,1,3], {
  	'dtype': 'float32'
  });
  // returns [ [ [~0.349,~0.104,~3.897] ], [ [~0.426,~4.594,~0.281] ] ]

Method

The algorithm used to generate gamma random variables is taken from a paper by Marsaglia & Tsang. It is very fast provided one has access to a performant uniform and normal number generator.

To generate the random standard normal variates, the module internally calls the normal-random which provides a very fast algorithm, the improved Ziggurat algorithm by Doornik, to sample from a normal distribution.

Reference:

Marsaglia, G., & Tsang, W. W. (2000). A simple method for generating gamma variables. ACM Transactions on Mathematical Software, 26(3), 363–372. doi:10.1145/358407.358414

Doornik, J. a. (2005). An Improved Ziggurat Method to Generate Normal Random Samples.

Examples

var random = require( 'distributions-gamma-random' ),
	out;

// Set seed
random.seed = 4;

// Plain arrays...

// 1x10:
out = random( 10 );

// 2x1x3:
out = random( [2,1,3] );

// 5x5x5:
out = random( [5,5,5] );

// 10x5x10x20:
out = random( [10,5,10,20] );

// Typed arrays...
out = random( 10, {
	'dtype': 'float32'
});

// Matrices...
out = random( [3,2], {
	'dtype': 'float64'
});

To run the example code from the top-level application directory,

$ node ./examples/index.js

Tests

Unit

Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:

$ make test

All new feature development should have corresponding unit tests to validate correct functionality.

Test Coverage

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

$ make test-cov

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

$ make view-cov

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License

MIT license.

Copyright

Copyright © 2015. The Compute.io Authors.