Multivariate Distributions

Compute, fit, and generate samples from vector-valued distributions

A multivariate distribution is a probability distribution that contains more than one random variable. The random variables might be correlated. Statistics and Machine Learning Toolbox™ offers several ways to work with multivariate distributions, including probability distribution objects, distribution functions, and interactive apps. For more information, see Working with Probability Distributions.

Objects

`gmdistribution`	Create Gaussian mixture model
`MultinomialDistribution`	Multinomial probability distribution object

Functions

expand all

Work with `gmdistribution` Object

`cdf`	Cumulative distribution function for Gaussian mixture distribution
`cluster`	Construct clusters from Gaussian mixture distribution
`mahal`	Mahalanobis distance to Gaussian mixture component
`pdf`	Probability density function for Gaussian mixture distribution
`posterior`	Posterior probability of Gaussian mixture component
`random`	Random variate from Gaussian mixture distribution

Copula Distribution Functions

`copulacdf`	Copula cumulative distribution function
`copulapdf`	Copula probability density function
`copulaparam`	Copula parameters as function of rank correlation
`copulastat`	Copula rank correlation
`copulafit`	Fit copula to data
`copularnd`	Copula random numbers

Wishart Distribution Functions

wishrnd Wishart random numbers

Inverse Wishart Distribution Functions

iwishrnd Inverse Wishart random numbers

Multivariate Normal Distribution Functions

`mvncdf`	Multivariate normal cumulative distribution function
`mvnpdf`	Multivariate normal probability density function
`mvnrnd`	Multivariate normal random numbers

Multivariate t Distribution Functions

`mvtcdf`	Multivariate t cumulative distribution function
`mvtpdf`	Multivariate t probability density function
`mvtrnd`	Multivariate t random numbers

Multinomial Distribution Functions

`mnpdf`	Multinomial probability density function
`mnrnd`	Multinomial random numbers

Topics

Generate Correlated Samples Using Copulas
Copulas are functions that describe dependencies among variables, and provide a way to create distributions that model correlated multivariate data.
Generate Correlated Data Using Rank Correlation
Use a copula and rank correlation to generate correlated data from probability distributions that do not have an inverse cdf function available, such as the Pearson flexible distribution family.
Simulate Dependent Random Variables Using Copulas
Use copulas to generate data from multivariate distributions with complicated relationships among the variables, or with the individual variables from different distributions.
Create Gaussian Mixture Model
Create a known, or fully specified, Gaussian mixture model (GMM) object.
Fit Gaussian Mixture Model to Data
Simulate data from a multivariate normal distribution, and then fit a Gaussian mixture model (GMM) to the data.
Simulate Data from Gaussian Mixture Model
Simulate data from a Gaussian mixture model (GMM) using a fully specified gmdistribution object and the random function.
Cluster Data Using Gaussian Mixture Model
Partition data into clusters with different sizes and correlation structures.
Inverse Wishart Distribution
The inverse Wishart distribution, which is based on the Wishart distribution, is used in Bayesian statistics as the conjugate prior for the covariance matrix of a multivariate normal distribution.
Multinomial Distribution
The multinomial distribution models the probability of each combination of successes in a series of independent trials.
Multivariate Normal Distribution
The multivariate normal distribution is a generalization of the univariate normal to two or more variables.
Multivariate t Distribution
The multivariate Student's t distribution is a generalization of the univariate Student's t to two or more variables.
Wishart Distribution
The Wishart distribution is a generalization of the univariate chi-square distribution to two or more variables.
Maximum Likelihood Estimation
The mle function computes maximum likelihood estimates (MLEs) for a distribution specified by its name and for a custom distribution specified by its probability density function (pdf), log pdf, or negative log likelihood function.
Negative Loglikelihood Functions
Find maximum likelihood estimates using negative loglikelihood functions.