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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 Examples |
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Choose Parametric Tests or Their Nonparametric Counterparts
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Cluster a Bivariate Dataset
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Compare Maximum-Likelihood and Cramér-von Mises Estimates
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Compare Nonparametric and Parametric Reliability Models
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Compare Two Models of Wind Speeds
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Compute a Complex Probability
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Compute a Two-Tailed Probability
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Compute Statistics from Censored and Truncated Data
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Construct a Kalman Filter for a Stochastic System
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Convert between Formal Moments
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Create a Correlation Table
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Create Confidence Envelopes about Nonparametric Density Estimates
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Create Paired Histograms for Comparing Data
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Decompose Mixture Models of Earthquake Magnitudes
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Estimate Multivariate Nonparametric Probabilities and Expectations
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Estimate Parameters and Test Goodness of Fit
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Expected Length of a Human Chromosome
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Find a Meeting Probability
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Find and Visualize a Linear Regression
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Find and Visualize Clusters in Data
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Find and Visualize Residuals for Fitted Models
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Find Operational Rules for a Data Center
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Fit Word Length Data to Distributions
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Improve the Manufacturing of LCD Displays
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Make a Histogram
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Make a Histogram of Stock Returns
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Model Claim Payments for Insurance
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Model Word Lengths by Binomial Distributions
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Perform Affine Transformations on a Normal Distribution
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Perform an Edgeworth Expansion to Approximate a Distribution
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Perform Tests of Location and Scale Simultaneously on Multiple Datasets
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Simulate a Derived Distribution
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Simulate Incomes with Dagum Distribution
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Solve Optimization Problems in Density Estimation
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Test for Goodness of Fit to Any Distribution or Dataset
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Truncate a Distribution
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Use a Gompertz Distribution as a Lifetime Model
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Use a Logistic Distribution to Simulate Fractional Change
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Use Component Mixtures to Model Multimodal Data
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Use Different Copula Kernels
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Visualize an Urn Model with Weighted Balls
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Visualize Distribution Functions for a Fitted Multivariate Distribution
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Visualize Optimal Parameter Values
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Visualize the Multivariate Poisson Distribution in 3D
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Visualize the Projected Lifetime of a Component
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Word Length Distribution in Various Languages
Reference
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
Distributions
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
Processes
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
