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Download a pdf copy of this help file here |
See also: Zero-modified counting distributions
Format: VoseSkellam(λ1, λ2, U)
A Skellam(λ1,
λ2) distribution returns discrete values
between -infinity and +infinity. This is a unique property among discrete
distributions. Examples of the Skellam distribution are shown below:
The Skellam distribution models the difference between two independent Poisson distributed variables as follows:
Skellam(λ1, λ2) = Poisson(λ1) - Poisson(λ2)
The Skellam distribution has a number of uses, essentially relating to the above formula. For example the difference in number of accidents (or murders, strikes, catastrophes, etc. – anything that occurs randomly in time) between, for example, two cities, two populations, two years, etc – where it is assumed that the expected rate of occurrence for the two variables are λ1 and λ2.
For the sports and games fans among you, it can be used to model the point spread between two teams where points are scored independently and in single units (like field hockey, ice hockey, soccer, chess, backgammon (if you ignore doubling) and baseball), but not where points are scored in ‘clusters’ (like rugby where a trial (5 points) may be followed by a conversion (2 points), cricket (1-6 runs from a hit), basketball where a basket is worth 1, 2 or 3 points depending on where the shot was taken from, or American football where a touchdown is worth 5 points, a try is worth 1 or 2 points, a field goal is worth 3 points, and a safety is worth 2 points).
When modeling or analyzing counting data, it is often desirable to modify the probability of zero of the discrete distribution we use, to more accurately model the probability of "no event occurring". A zero-inflated Skellam distribution (increase the probability of zero) is also available in ModelRisk.
VoseSkellam generates values from this distribution or calculates a percentile. Professional and Industrial editions only.
VoseSkellamObject constructs a distribution object for this distribution. Professional and Industrial editions only.
VoseSkellamProb returns the probability mass or cumulative distribution function for this distribution. Professional and Industrial editions only.
VoseSkellamProb10 returns the log10 of the probability mass or cumulative distribution function. Professional and Industrial editions only.
VoseSkellamFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution. Professional and Industrial editions only.
VoseSkellamFitObject constructs a distribution object of this distribution fitted to data. Professional and Industrial editions only.
VoseSkellamFitP returns the parameters of this distribution fitted to data. Professional and Industrial editions only.