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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 models are now universally used across all areas of science, technology and business.

Mathematica uses symbolic distributions and processes as models for random variables and random processes. The models can 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.

Featured ExamplesFeatured Examples |


Probability compute probabilities of predicates

Expectation compute expectations of expressions

NProbability ▪ NExpectation ▪ Distributed (Distributed) ▪ Conditioned (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


NormalDistribution parametric distributions ...

SmoothKernelDistribution nonparametric distributions ...

TransformedDistribution derived distributions ...

Random Processes »

RandomFunction simulate a random process

TemporalData represent one or several time-series data

EstimatedProcess estimate process parameters from data

SliceDistribution ▪ Mean ▪ CovarianceFunction


PoissonProcess parametric processes ...

ARMAProcess time series processes ...

ItoProcess stochastic differential equation processes ...

Survival Analysis »

EventData represent censored and truncated data

Median ▪ SurvivalModelFit ▪ CoxModelFit

Reliability Analysis »

ReliabilityDistribution reliability block diagram-based lifetime distribution

FailureDistribution ▪ BirnbaumImportance