Define a spliced distribution with a normal body and a Pareto tail:

Probability density function:

Find the mean and variance of a spliced distribution:

Compare with the values obtained by using a random sample:

Add symmetric exponential tails to normal distribution:

Distribution functions:

Since distribution is symmetric, all odd moments are 0:

Even moments:

Create a Student distribution with a heavier right tail:

Probability density function:

Generate a set of pseudorandom numbers that follow this distribution:

Compare the histogram of the sample to the PDF:

Generate a set of pseudorandom numbers following lognormal distribution with exponential tails:

Estimate the tail parameter:

Compare the histogram of the sample with the PDF:

Splicing QuantityDistribution with compatible units yields QuantityDistribution:

Plot the probability density function:

Create a spliced distribution, with normal distribution in the center and tails of a heavy-tail distribution:

Find spliced distribution with continuous PDF by adjusting the weights:

Equate limits at both points of possible discontinuity:

Substitute the solution:

Plot PDF of the spliced distribution:

A spliced distribution is related to ProbabilityDistribution and TruncatedDistribution:

Represent as a linear combination of truncated PDFs:

A spliced distribution is related to MixtureDistribution and TruncatedDistribution:

Represent as a mixture of truncated distributions:

SplicedDistribution with one distribution simplifies to TruncatedDistribution: