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.

Probability — compute probabilities of predicates

Expectation — compute expectations of expressions

NProbability  ▪  NExpectation  ▪  Distributed ()  ▪  Conditioned ()

Random Variables »

RandomVariate — generate random variates from a distribution

EstimatedDistribution — estimate parametric or derived distribution from data

DistributionFitTest — test how well data and a distribution fit

PDF  ▪  CDF  ▪  Mean  ▪  Variance  ▪  Around

Distributions

NormalDistribution — parametric distributions ...

SmoothKernelDistribution — nonparametric distributions ...

TransformedDistribution — derived distributions ...

Random Processes »

RandomFunction — simulate a random process

TemporalData — represent one or several time-series datasets

EstimatedProcess — estimate process parameters from data

SliceDistribution  ▪  Mean  ▪  CovarianceFunction

Processes

PoissonProcess — parametric processes ...

ARMAProcess — time series processes ...

ItoProcess — stochastic differential equation processes ...

Spatial Point Processes & Statistics »

RandomPointConfiguration — simulate a random point process

SpatialPointData — spatial annotated point data

EstimatedPointProcess — estimate point process from data

PointDensity  ▪  RipleyK  ▪  SpatialRandomnessTest  ▪  ...

Point Processes »

PoissonPointProcess  ▪  HardcorePointProcess  ▪  MaternPointProcess  ▪  ...

Survival Analysis »

EventData — represent censored and truncated data

Median  ▪  SurvivalModelFit  ▪  CoxModelFit

Reliability Analysis »

ReliabilityDistribution — reliability block diagram-based lifetime distribution

FailureDistribution  ▪  BirnbaumImportance