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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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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:
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:
The point spread distribution:
Compute the probability that the Cardinals will score at least 2 more runs than the Cubs in a game:
The expected margin of victory, given the Cubs beat the Cardinals by more than 1 run:
The number of packets arriving to a loading dock follows a PoissonDistribution with mean 30 per hour. The packets are then removed from the dock following a PoissonDistribution with mean 25 per hour. Find the distribution of the number of packets remaining on the dock:
Simulate the number of packets on the dock for the next 100 hours:
Skellam distribution is closed under sum:
Skellam distribution is closed under difference:
Relationships to other distributions:
The difference of two Poisson-distributed variables has a Skellam distribution:
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