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Binomial Equations

Crystal Ball parameter restrictions



A Binomial(p,n) distribution returns discrete values between 0 and n. Examples of the Binomial distribution are shown below:





The Binomial distribution models the number of successes from n independent trials where there is a probability p of success in each trial (as explained in the section on the Binomial process).


Blood samples that have zero, or >0 antibodies;

Approximation to a hypergeometric distribution


The following links lead to just some of the examples and models in ModelAssist that use the binomial distribution:


2017-11-06_21-58-04_Conditional logic

Sampling from a liquid

Distribution fitting of threshold data

Bayesian prior

Test result


The Binomial distribution makes the assumption that the probability p does not change the more trials are performed. That would imply that my aim doesn't get better or worse. It wouldn't be a good estimator, for instance, if the chance of success improved with the number of trials.


The Binomial distribution was first discussed by Bernoulli (1713). It is related to the 2017-11-06_21-56-49_Beta and 2017-11-06_21-56-47_Negative Binomial distributions, all of which have their basis in the Binomial process where the Binomial distribution is also derived. The 2017-11-06_21-56-41_ Bernoulli distribution is a special case of the Binomial with n = 1 i.e.: Bernoulli(p) = Binomial(p,1) that is used to model risk events.