Find the second univariate marginal distribution:
Multivariate marginals depend on the coordinate order given:
Univariate marginals behave as univariate distributions:
Find distribution functions:
Multivariate marginals behave like a multivariate distribution:
Find distribution functions:
Special moments are computed for each univariate marginal distribution:
Compare moments of marginal distributions with the moment of original distribution:
A general multivariate moment cannot typically be found from marginal moments:
Quantile functions can be computed for univariate marginal distributions:
Find the quantile functions:
Or special medians:
Generate random variates from
MarginalDistribution:
Compare the histogram to the plot of the PDF of the marginal distribution:
Estimate distribution parameters:
Define a trivariate probability distribution:
Find marginal distributions:
Find the covariance matrix of
:
The variances of the marginals form the diagonal of the covariance matrix of
:
The marginal distributions of many multivariate parametric distributions automatically simplify:
The univariate marginals follow
BetaDistribution:
The multivariate marginals follow
DirichletDistribution:
In some cases, marginal distributions will not automatically simplify:
Univariate marginals simplify to a
BinomialDistribution:
The multivariate marginals do not simplify:
The resulting marginal can still be used like any other distribution:
Find marginals of an
EmpiricalDistribution:
Cumulative distribution function of the marginal distributions:
Find marginals of a
HistogramDistribution:
Compare to the histograms of the components:
Find the marginal distribution of a
MarginalDistribution:
The second marginal of
is the third marginal of
:
Find marginals of a
CopulaDistribution:
Find marginals of a
TruncatedDistribution:
Probability density function:
Find marginals of a
MixtureDistribution:
Each marginal distribution is the mixture of marginals:
Compare with the marginal distributions of the components:
Marginals of a
MixtureDistribution are mixtures of marginals:
Plot a probability density function for both marginals:
Create a bivariate distribution using marginal distributions:
Compare a PDF of the original distribution
with the
ProductDistribution of marginals:
Compare covariance matrices:
Find marginal distributions of a
TransformedDistribution:
Find marginal distributions of a
ParameterMixtureDistribution:
Visualize the probability density function:
Find marginal distributions of an
OrderDistribution:
Probability density function:
Mean:
Variance:
Marginals of multivariate
DiscreteUniformDistribution again follow a uniform distribution:
Multivariate marginals again follow multivariate Poisson distribution:
Multivariate marginals of
MultinormalDistribution are multivariate normal:
Marginals of multivariate
UniformDistribution follow uniform distribution:
One-dimensional marginals of
DirichletDistribution follow
BetaDistribution:
Multivariate marginals of
DirichletDistribution again follow Dirichlet distribution:
Marginals of
ProductDistribution are the component distributions:
One-dimensional marginal:
A two-dimensional marginal is also defined by
ProductDistribution:
Univariate marginals of a
CopulaDistribution are the marginals used in the specification:
Marginal distributions of a
MixtureDistribution are the mixtures of component marginals:
coordinate from the multivariate distribution dist.
coordinates.
, the PDF of MarginalDistribution
is given by 
where 
. 
, the PDF of MarginalDistribution
is given by 
where 
.
and 
. On a day there are on average 10 car accidents on campus and the joint distribution of the number of accidents per day in both cities is:
for 30 days:
-variable multivariate distribution has 
proper marginal distributions: 
as 
: 
as 
:
as 
: 
as 
:
:
:
is a submatrix of the covariance of 
:
EXAMPLES
Basic Examples 
Scope 