This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# SkellamDistribution

 SkellamDistribution represents a Skellam distribution with shape parameters and .
• The probability for integer value in a Skellam distribution is proportional to .
• SkellamDistribution is the distribution for where the are independent Poisson distributed with parameter .
Probability density function:
Cumulative distribution function:
Mean and variance:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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 Scope   (7)
Generate a set of pseudorandom numbers that are Skellam distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare a density histogram of the sample with the PDF of the estimated distribution:
Skewness:
Kurtosis:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (3)
The CDF of SkellamDistribution is an example of a right-continuous function:
The Chicago Cubs and St. Louis Cardinals scored an average of 4.72 and 4.88 runs per game, respectively, between the 2004 and 2008 seasons. Assume the runs for each team are independent and distributed according to a PoissonDistribution with the mean, respectively: