VoseBinomialP | Vose Software


=VoseBinomialP(s,n,ProcessExists, U)



Example model

This function generates values for the classical statistics uncertainty distribution for a binomial probability p estimated from data as described on this page.

  • s - the number of successes.

  • n - the number of trials.

  • ProcessExists - an optional boolean parameter (TRUE/FALSE) that controls the function's behavior for s=0 or s=n. TRUE specifies one knows the estimated probability is neither 0 nor 1. FALSE (default) means one does not know.

  • U - optional parameter specifying the cumulative percentile of the distribution. If omitted the function generates random values.

Note that the ProcessExists parameter only has influence in the cases s=0 or s=n.


A certain company sends out transactional documents (like bank statements, insurance policy documents, etc.) to clients. It does a survey of 1000 documents, tracking if they were properly completed and delivered to the right address on time. It found all 1000 documents were successfully processed. Given this amount of data it would like to know the probability that a document might fail to be properly processed.

The uncertainty distribution for the probability then can be found with the formula (Case 1):


This is the company's uncertainty about the probability without knowing if there is in fact a possibility of the system failing (ProcessExists = 0).

Now suppose the company receives a complaint letter from a client saying that an error occurred with his/her transactional document. This now means that we know for sure that the process of printing and sending out a document incorrectly exists (ProcessExists = 1). The uncertainty distribution for the probability can now be expressed by the formula (Case 2):


We could have defined a 'success' as a correctly processed document, in which case we have the probability of success (the probability a document will be correctly processed, as:

Case 1: VoseBinomialP(1000,1000,0)

Case 2: VoseBinomialP(1000,1000,1)

The Bayesian equivalent to estimating a probability is described here. A comparison of the classical and Bayesian methods can be found here.