Define a product of two independent continuous distributions:
The PDF is the product of the component PDFs:
Product of discrete distributions:
The PDF is the product of the component PDFs:
Define a product distribution in which three components are repeated:
Probability density function for the four-dimensional product distribution:
Product distribution with both continuous and discrete components:
Draw a random sample from this distribution:
Estimate the distribution parameters for the components using the random sample:
Define a general product distribution with few repeated components:
Compare to a random sample:
Product of multivariate continuous distributions:
Probability density function:
Verify that the integral of the PDF is 1:
Product of multivariate discrete distributions:
Compute the variance of the distribution:
Compare with the values obtained by using a random sample:
Create a bivariate normal distribution with independent components:
Probability density function:
Define a two-dimensional Laplace distribution:
Probability density function:
Mean and variance:
Define product distribution of independent
PoissonDistribution:
Probability density function:
Covariance:
The
MultivariatePoissonDistribution does not have independent components:
The assumptions:
Create the product distribution of two independent examples of
StudentTDistribution:
Generate random sample:
Goodness-of-fit test:
Compute properties with symbolic parameters:
Distribution functions:
Special moments:
Moments with closed forms for symbolic order:
Other moments can be obtained numerically:
Generating functions:
Find product distribution of the marginal distributions:
Probability density function of
:
is a
MultinormalDistribution with a diagonal covariance matrix:
Compare to the product of original distributions:
Create a sample from
and define
SmoothKernelDistribution for this sample:
Compare all three distributions:
Define a product of
EmpiricalDistribution:
Plot the probability density function and cumulative distribution function:
Define a product distribution with
HistogramDistribution:
Probability denstiy function:
Define a product with a
CensoredDistribution:
Compose product distribution from marginals:
Probability density function:
It is the same as for binormal distribution with no correlation:
The components of product distribution are assumed to be independent, hence the original distribution cannot be recovered when
is not zero:
Create the product distribution from a
MixtureDistribution:
Probability density function:
Mean and variance:
Find the product distribution of minimum and maximum
OrderDistribution:
Probability density function:
Plot density function for fixed
:
Define a product distribution of a
ParameterMixtureDistribution:
Product distribution is used as an input for a
TransformedDistribution:
Find the product distribution of a
TransformedDistribution:
Probability density function:
Find the product distribution of a
TruncatedDistribution:
Variance depends on the truncation interval:
Compare the PDF to the product of distributions that are not truncated:
Find the product distribution of a
TruncatedDistribution:
Compare the PDF with the product distribution of two Poisson distributions:
Truncation influences the direction and value of skewness:
, 
, ....
is given by 
where 
is the PDF of 
, 
is the PDF of 
, etc. 
indicates that 
is repeated n times. 
can be any combination of univariate, multivariate, continuous, or discrete distributions. 
:
EXAMPLES
Basic Examples 
Scope 