Frequency of events in risk modelling: the inverse binomial as an alternative for Poisson in Excel

[@zenlifestyleandmannersshow6892]

Clear and concise

[@StachanovSolutionsServices]

Thanks!

[@surabhiyadav6750]

I did not understand why can't we use Poisson? Since banks use Poisson itself to generate frequency in LDA.

[@StachanovSolutionsServices]

Thanks for your question. There are similarities and differences between the binomial and the Poisson distributions. You'll find a good explanation here:
www.statology.org/binomial-vs-poisson-distribution-similarities-differences/
Best, André

[@chrisdickinson4576]

It is easier to use the normal approximation for the Poisson. There is a norm inv function in excels: Round(NormInv(Rand(),Avg, sqrt(Avg)), 0) where Avg is the Average of the Poisson you want to simulate. (When average is high).

[@FenderAddict93]

I don't see how this closely approximates inverse Poisson. Care to elaborate why?

[@chrisdickinson4576]

@@FenderAddict93 The Normal Distribution can be used to approximate the Poisson due to the central limit theorem - google normal approximation for the POisson.

[@FenderAddict93]

@@chrisdickinson4576 As you’ve mentioned, the normal approximation is only applicable if the Lambda parameter is high enough. Which means it fails to capture a good estimate/approximation if we were to have small Lambda value.
In this sense, wouldn’t the inverse Binomial be a better method to use? Since it only requires a large number of trials for it to approximate Poisson distribution.

[@chrisdickinson4576]

@@FenderAddict93 For a smaller average you are better off just inverting the the Poisson Distribution CDF using a bit of VBA. The only approximation that makes any sense is the Normal Approximation. Otherwise just use a bit of code to invert the Poisson CDF.