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See also: Poisson distribution
Format: VoseBurntFingerPoisson(l1 ,l2 , U)
A BurntFingerPoisson(l1
,l2)
distribution returns discrete values from 0 to +infinity:
The Burnt Finger Poisson distribution models the total number of incidents that may occur in a period under the following rules: >
At the beginning of the period, incidents may occur according to a Poisson process with mean l1;
If an incident does occur, then subsequent incidents may occur according to a Poisson process with mean l2;
l2 < l1.
This type of situation occurs when, for example, an individual has an expected rate of accidents l1, but if an accident occurs the individual will become more careful (his/her ‘fingers got burned’) so that for the rest of the modeled time a new, lower expected accident rate l2 applies.
Looking at the above chart can help better understand the BurntFingerPoisson. The probability of zero events is the same for all three distributions since it is the probability of zero for a Poisson(3). Since Poisson(3) = BurntFingerPoisson(3,3), we can compare the effect of the decrease in l2 between distributions: the lower l2 the smaller the probability of high numbers of events.
It can be useful to compare the distribution fits for count data from a variety of Poisson-related distributions like the Poisson, Pólya, Delaporte, ZIPoisson, PoissonUniform and BurntFingerPoisson because they allow you to test different possible mechanisms that may be in place.
It is particularly computationally intensive to simulate from, or calculate probabilities for, the BurntFingerPoisson distribution, especially for large values (e.g. >20) of l2. A very small amount of approximation has been implemented in ModelRisk for l2 > 100 to make probability calculations feasible. If possible avoid simulating using the U parameter which can slow down simulating from the BurntFingerPoisson enormously.
VoseBurntFingerPoisson generates values from this distribution or calculates a percentile. Professional and Industrial editions only.
VoseBurntFingerPoissonObject constructs a distribution object for this distribution. Professional and Industrial editions only.
VoseBurntFingerPoissonProb returns the probability mass or cumulative distribution function for this distribution. Professional and Industrial editions only.
VoseBurntFingerPoissonProb10 returns the log10 of the probability mass or cumulative distribution function. Professional and Industrial editions only.
VoseBurntFingerPoissonFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution. Professional and Industrial editions only.
VoseBurntFingerPoissonFitObject constructs a distribution object of this distribution fitted to data. Professional and Industrial editions only.
VoseBurntFingerPoissonFitObject returns the parameters of this distribution fitted to data. Professional and Industrial editions only.