Distributions

Collection of probability distributions.

This modules provides functions to evaluate the CDF, PDF / PMF and quantile functions for a wide range of discrete and continuous probability distributions. In addition, it implements random number generators, moment-generating functions and facilities to retrieve distribution properties such as the moments of the respective distribution.

Installation

$ npm install distributions.io

Usage

var dist = require( 'distributions.io' );

Common Interface

Distributions

• Discrete Distributions
  • .binom (Binomial)
    • pmf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .geom (Geometric)
    • pmf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .hypergeom (Hypergeometric)
    • pmf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .nbinom (Negative binomial)
    • pmf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .pois (Poisson)
    • pmf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
• Continuous Distributions
  • .beta (Beta)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .cauchy (Cauchy)
    • pdf(), cdf(), quantile()
    • random()
    • median(), entropy()
  • .chisq (Chi-Squared)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .erlang (Erlang)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .exp (Exponential)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .f (Fisher's F)
    • pdf(), cdf(), quantile()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .gamma (Gamma)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .gumbel (Gumbel)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .invgamma (Inverse-Gamma)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .laplace (Laplace)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .logistic (Logistic)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .lnorm (Log-Normal)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .rayleigh (Rayleigh)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .t (Student T)
    • pdf(), cdf(), quantile()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .unif (Continuous Uniform)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .norm (Normal)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .pareto (Pareto Type I)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .triangular (Triangular)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()
  • .weibull (Weibull)
    • pdf(), cdf(), quantile(),mgf()
    • random()
    • mean(), median(), variance(), skewness(), ekurtosis(), entropy()

Examples

var dist = require( 'distributions.io' ),
	out;

// Generate 30 standard normal random variates:
out = dist.norm.random( 30 );

// Evaluate the PDF of a exponential distribution with lambda=2 at 0:
out = dist.exp.pdf( 0, {lambda: 2} );

// Retrieve the excess kurtosis of a Poisson random variable with lambda = 3:
out = dist.poisson.ekurtosis( 3 );

// Evaluate the CDF of a standard normal for an array of values:
out = dist.norm.cdf( [-3,-2,-1,0,1,2,3] );

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

License

MIT license.

Copyright

Copyright © 2015. The Distributions.io Authors.