Probability & Statistics

Probability and statistics are used to model uncertainty from a variety of sources, such as incomplete or simplified models. Yet you can build useful models for aggregate or overall behavior of the system in question. These types of models are now universally used across all areas of science, technology, and business. 
The Wolfram Language uses symbolic distributions and processes as models for random variables and random processes. The models can be automatically computed from data or analytically constructed from a rich library of built-in distributions and processes. The models can be simulated or used to directly answer a variety of questions.

(RefLink[Probability, paclet:ref/Probability]) — compute probabilities of predicates

(RefLink[Expectation, paclet:ref/Expectation]) — compute expectations of expressions

(OrangeLink[Random Variables », paclet:guide/RandomVariables])

(RefLink[RandomVariate, paclet:ref/RandomVariate]) — generate random variates from a distribution

(RefLink[EstimatedDistribution, paclet:ref/EstimatedDistribution]) — estimate parametric or derived distribution from data

(RefLink[DistributionFitTest, paclet:ref/DistributionFitTest]) — test how well data and a distribution fit

Distributions

(RefLink[NormalDistribution, paclet:ref/NormalDistribution]) — parametric distributions ...

(RefLink[SmoothKernelDistribution, paclet:ref/SmoothKernelDistribution]) — nonparametric distributions ...

(RefLink[TransformedDistribution, paclet:ref/TransformedDistribution]) — derived distributions ...

(OrangeLink[Random Processes », paclet:guide/RandomProcesses])

(RefLink[RandomFunction, paclet:ref/RandomFunction]) — simulate a random process

(RefLink[TemporalData, paclet:ref/TemporalData]) — represent one or several time-series datasets

(RefLink[EstimatedProcess, paclet:ref/EstimatedProcess]) — estimate process parameters from data

Processes

(RefLink[PoissonProcess, paclet:ref/PoissonProcess]) — parametric processes ...

(RefLink[ARMAProcess, paclet:ref/ARMAProcess]) — time series processes ...

(RefLink[ItoProcess, paclet:ref/ItoProcess]) — stochastic differential equation processes ...

(OrangeLink[Survival Analysis », paclet:guide/SurvivalAnalysis])

(RefLink[EventData, paclet:ref/EventData]) — represent censored and truncated data

(OrangeLink[Reliability Analysis », paclet:guide/Reliability])

(RefLink[ReliabilityDistribution, paclet:ref/ReliabilityDistribution]) — reliability block diagram-based lifetime distribution