PoissonUniform distribution | Vose Software

PoissonUniform distribution

Format: PoissonUniform(min,max,)


A PoissonUniform(min,max) is a version of the Poisson (λ) distribution for which the mean λ is itself a Uniform(min,max) random variable:

PoissonUniform(min,max) = Poisson (Uniform (min,max))



The PoissonUniform distribution can be used in place of the Poisson distribution for modeling counts of events where the observed variation between periods is greater than would be predicted by a Poisson distribution. For a Poisson distribution, Variance/mean is given by:


and for the PoissonUniform it is:



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.

ModelRisk functions added to Microsoft Excel for the Hypergeometric-D distribution

VosePoissonUniform generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VosePoissonUniformObject constructs a distribution object for this distribution.

VosePoissonUniformProb returns the probability mass or cumulative distribution function for this distribution.

VosePoissonUniformProb10 returns the log10 of the probability mass or cumulative distribution function.

VosePoissonUniformFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VosePoissonUniformFitObject constructs a distribution object of this distribution fitted to data.

VosePoissonUniformFitP returns the parameters of this distribution fitted to data.


Poisson Uniform distribution equations