Define various truncations for a univariate continuous distribution:

The resulting PDF is 0 outside the truncation region:

Define various truncations for a univariate discrete distribution:

The left endpoint is not included, but the right endpoint is included:

Define a right-truncated distribution:

Compare PDFs:

Define a left-truncated distribution:

Compare probability density functions:

Compare means:

Compare standard deviations:

Define a doubly truncated distribution:

Compare means:

Compare variances:

Define a truncated multivariate continuous distribution:

Compute the expectation of an expression for this distribution:

Find a few moments:

Define a truncated multivariate discrete distribution:

Compare probabilities for a point outside the truncation region:

Generate a random sample:

Compare the means:

Define a truncated multivariate discrete distribution:

Compare skewness:

Compare kurtosis:

Estimate a truncation interval using

EstimatedDistribution:

Fit a truncated normal:

Define a left-truncated continuous distribution:

Compare the probability density functions:

Cumulative distribution function of the truncated exponential distribution:

Statistical measures:

Compare to the original distribution:

Define a right-truncated discrete distribution:

Compare the PDFs:

The truncated distribution is the same as the following:

Define a truncation of a

UniformDistribution:

Probability density function:

Compare to the uniform distribution defined on the truncation interval:

Probability density function:

Compare to the uniform distribution defined on the truncation interval:

Truncation does not include the left endpoint, hence the resulting discrete distribution:

Define a truncated binormal distribution:

Compare the PDFs for the binormal distribution and the truncated version:

Probability density function of the truncated binormal:

Characteristic function:

Define a discrete multivariate truncated distribution:

Perform statistical operations on this distribution:

Generate a set of pseudorandom numbers from a truncated distribution:

Compare the histogram to the PDF:

Compare probability density functions:

Compare cumulative distribution functions:

Probability density function:

Find a probability density function:

Identify as a truncated distribution:

Define a truncated

CopulaDistribution:

Define a truncated

MixtureDistribution:

Compare probability density functions:

Define a truncated

OrderDistribution:

Find the probability that the maximum of a Poisson sample is greater than 6, assuming it is greater than 5:

Find the probability that the maximum is greater than 6 without assuming it is greater than 5:

Compare

with the transformation of the truncated normal:

Compare PDFs:

Find the probabilities of most-likely values for both distributions:

Define a truncated

ProductDistribution:

Compare the probability density functions:

Compare with the PDF of the product of the truncated distributions:

Define a truncated

MarginalDistribution:

Compare the probability density functions:

Define a truncated

CensoredDistribution:

Compare the probability density functions:

NormalDistribution truncated to a positive axis follows a

HalfNormalDistribution:

ParetoDistribution is closed under truncation:

UniformDistribution is closed under truncation:

DiscreteUniformDistribution is closed under truncation:

ZipfDistribution is closed under truncation: