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.
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
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
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