This is known as a Poisson distribution and the mathematical proof can be viewed here. n → ∞ and the probability is decreasing p → 0 in such a way that n p → λ. Returning to the n, p of the Binomial distribution, this would more closely model an infinite amount of trials i.e. Let’s use λ to denote the mean number of events. Now why is the binomial situation inappropriate in this case? The binomial distribution counts the number of occurrences in a set amount of trials whereas in this case there may be infinite events. The expected average number is known over a certain time period.The events cannot occur simultaneously, there is only one fish on the line.A large number of fish might get caught, but with small likelihood - I could theoretically amass 5,000 fish in a day though it is highly unlikely.Neither would I get portions of fish – it is all or nothing.Sometimes catching a fish might not happen, but I would never receive -2 fish on any given day.Let’s look at the limiting factors in modelling this: a fish deciding to be caught has no bearing on the decision of another to bite. The fishes are presumed independent from each other, i.e. Over long observation, I notice that I net four fish a day. Let us look at modelling independent events that occur at a known and constant rate. This article looks at calculating the inverse of a Poisson distribution for scenario modelling but with the caveat this is a simple, pragmatic approach for non-academics.Ĭontinuing on from Simulation Stimulation, let us look at another way to model scenarios.

CrimeStat: CrimeStat has Poisson, Poisson NB1, Poisson-Gamma(negative binomial), and Poisson-Lognormal regression models.Cecile Nguyen likes fishing for answers.

Stata: Stata has a procedure for Poisson regression named 'poisson', and for panel data 'xtpoisson'.

SPSS: In SPSS, Poisson regression is done by using the GENLIN command.

SAS: Poisson regression in SAS is done by using GENMOD, HPGENSELECT, COUNTREG, GLIMMIX, and NLMIXED.

R: The function for fitting a generalized linear model in R is glm(), and can be used for Poisson Regression.

mPlus: mPlus allows for Poisson regression using the command COUNT IS when specifying the data.

One of the Excel Add-ins for Poisson regression is XPost

Microsoft Excel: Excel is not capable of doing Poisson regression by default.MATLAB Statistics Toolbox: Poisson regression can be performed using the 'glmfit' and 'glmval' functions.GenStat: Poisson regression is a standard option of the regression section, using the 'MODEL', 'FIT' and associated commands it is also available in the 'Stats > Regression Analysis > Generalized Linear Models' menu.Some statistics packages include implementations of Poisson regression. This technique, similar to ridge regression, can reduce overfitting. 2 Maximum likelihood-based parameter estimation.

Poisson regression excel