Probability -- basic probability functions

Description

This package provides a number of basic probability functions. In particular, for both discrete and continuous probability distributions, there are the following four functions:

density: probability density (or mass) function
probability: cumulative distribution function
quantile: quantile function
random(ProbabilityDistribution): generate random samples

A variety of common probability distributions are supported.

Discrete distributions

Continuous distributions

You may also define your own probability distributions using discreteProbabilityDistribution and continuousProbabilityDistribution.

Caveat

As is always the case when working with real numbers in Macaulay2, unexpected results may occur due to the limitations of floating point arithmetic.

Author

Doug Torrance <[email protected]>

Certification

Version 0.3 of this package was accepted for publication in volume 14 of Journal of Software for Algebra and Geometry on 2024-01-23, in the article The Probability package for Macaulay2 (DOI: 10.2140/jsag.2024.14.51). That version can be obtained from the journal.

Version

This documentation describes version 0.5 of Probability.

Citation

If you have used this package in your research, please cite it as follows:

@misc{ProbabilitySource,
  title = {{Probability: basic probability functions. Version~0.5}},
  author = {Doug Torrance},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

@article{ProbabilityArticle,
  title = {{The Probability package for \emph{Macaulay2}}},
  author = {Doug Torrance},
  journal = {Journal of Software for Algebra and Geometry},
  volume = {14},
  year = {2024},
}

Exports

Types
- ContinuousProbabilityDistribution -- see ProbabilityDistribution -- probability distribution class
- DiscreteProbabilityDistribution -- see ProbabilityDistribution -- probability distribution class
- ProbabilityDistribution -- probability distribution class
Functions and commands
- betaDistribution -- beta distribution
- bernoulliDistribution -- see binomialDistribution -- binomial distribution
- binomialDistribution -- binomial distribution
- chiSquaredDistribution -- chi-squared distribution
- continuousProbabilityDistribution -- construct a continuous probability distribution
- density -- probability density (or mass) function
- discreteProbabilityDistribution -- construct a discrete probability distribution
- exponentialDistribution -- exponential distribution
- fDistribution -- F-distribution
- gammaDistribution -- gamma distribution
- geometricDistribution -- geometric distribution
- hypergeometricDistribution -- hypergeometric distribution
- negativeBinomialDistribution -- negative binomial distribution
- normalDistribution -- normal distribution
- poissonDistribution -- Poisson distribution
- probability -- cumulative distribution function
- quantile -- quantile function
- tDistribution -- Student's t-distribution
- uniformDistribution -- continuous uniform distribution
Methods
- betaDistribution(Number,Number) -- see betaDistribution -- beta distribution
- bernoulliDistribution(Number) -- see binomialDistribution -- binomial distribution
- binomialDistribution(ZZ,Number) -- see binomialDistribution -- binomial distribution
- chiSquaredDistribution(Number) -- see chiSquaredDistribution -- chi-squared distribution
- continuousProbabilityDistribution(Function) -- see continuousProbabilityDistribution -- construct a continuous probability distribution
- density(DiscreteProbabilityDistribution,Number) -- see density -- probability density (or mass) function
- density(ProbabilityDistribution,Number) -- see density -- probability density (or mass) function
- discreteProbabilityDistribution(Function) -- see discreteProbabilityDistribution -- construct a discrete probability distribution
- exponentialDistribution(Number) -- see exponentialDistribution -- exponential distribution
- fDistribution(Number,Number) -- see fDistribution -- F-distribution
- gammaDistribution(Number,Number) -- see gammaDistribution -- gamma distribution
- geometricDistribution(Number) -- see geometricDistribution -- geometric distribution
- hypergeometricDistribution(ZZ,ZZ,ZZ) -- see hypergeometricDistribution -- hypergeometric distribution
- negativeBinomialDistribution(Number,Number) -- see negativeBinomialDistribution -- negative binomial distribution
- normalDistribution(Number,Number) -- see normalDistribution -- normal distribution
- poissonDistribution(Number) -- see poissonDistribution -- Poisson distribution
- probability(DiscreteProbabilityDistribution,Number) -- see probability -- cumulative distribution function
- probability(ProbabilityDistribution,Number) -- see probability -- cumulative distribution function
- net(ProbabilityDistribution) -- see ProbabilityDistribution -- probability distribution class
- quantile(DiscreteProbabilityDistribution,Number) -- see quantile -- quantile function
- quantile(ProbabilityDistribution,Number) -- see quantile -- quantile function
- random(ProbabilityDistribution) -- randomly generate samples from probability distribution
- tDistribution(Number) -- see tDistribution -- Student's t-distribution
- uniformDistribution(Number,Number) -- see uniformDistribution -- continuous uniform distribution
Symbols
- DensityFunction -- probability density function
- DistributionFunction -- cumulative distribution function
- LowerTail -- whether to computer lower tail probabilities
- QuantileFunction -- quantile function
- RandomGeneration -- random generation function
- Support -- support for probability distribution

For the programmer

The object Probability is a package, defined in Probability.m2.

The source of this document is in Probability.m2:473:0.