ProbabilityDistribution -- probability distribution class

Description

This is the class of which all probability distribution objects belong. ProbabilityDistribution is an abstract class defining the interface and should not be used directly. Instead, its subclasses DiscreteProbabilityDistribution and ContinuousProbabilityDistribution should be used.

ProbabilityDistribution objects are hash tables containing six key-value pairs:

DensityFunction: The probability mass or density function (for discrete or continuous distributions, respectively). Do not use this directly. Instead, use density.
DistributionFunction: The cumulative distribution function. Do not use this directly. Instead, use probability.
QuantileFunction: The quantile function. Do not use this directly. Instead, use quantile.
RandomGeneration: A function to generate random samples of the distribution. Do not use this directly. Instead, use random(ProbabilityDistribution).
Support: A sequence of two numbers, the lower and upper bound of the support of the distribution.
Description: A string containing a description of the distribution. This is the return value when a ProbabilityDistribution object is passed to net.

i1 : Z = normalDistribution()

o1 = N(0,1)

o1 : ContinuousProbabilityDistribution

i2 : ancestors class Z

o2 = {ContinuousProbabilityDistribution, ProbabilityDistribution, HashTable,
     ------------------------------------------------------------------------
     Thing}

o2 : List

i3 : peek Z

o3 = ContinuousProbabilityDistribution{DensityFunction => FunctionClosure[/usr/local/share/Macaulay2/Probability.m2:360:10-360:72]     }
                                       Description => N(0,1)
                                       DistributionFunction => FunctionClosure[/usr/local/share/Macaulay2/Probability.m2:361:34-362:52]
                                       QuantileFunction => FunctionClosure[/usr/local/share/Macaulay2/Probability.m2:363:30-364:53]
                                       RandomGeneration => FunctionClosure[/usr/local/share/Macaulay2/Probability.m2:366:31-367:73]
                                       Support => (-infinity, infinity)

To create a ProbablityDistribution object, use one of the constructor methods, discreteProbabilityDistribution, continuousProbabilityDistribution, or any of the various built-in methods for common distributions.

Types of probability distribution :

ContinuousProbabilityDistribution
DiscreteProbabilityDistribution

Methods that use a probability distribution :

density(ProbabilityDistribution,Constant) -- see density -- probability density (or mass) function
density(ProbabilityDistribution,Number) -- see density -- probability density (or mass) function
probability(ProbabilityDistribution,Constant) -- see probability -- cumulative distribution function
probability(ProbabilityDistribution,Number) -- see probability -- cumulative distribution function
net(ProbabilityDistribution)
quantile(ProbabilityDistribution,Constant) -- see quantile -- quantile function
quantile(ProbabilityDistribution,Number) -- see quantile -- quantile function
random(ProbabilityDistribution) -- randomly generate samples from probability distribution

For the programmer

The object ProbabilityDistribution is a type, with ancestor classes HashTable < Thing.