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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).


The binomial distribution has an enormous number of uses. Beyond simple binomial processes, many other stochastic processes can be usefully reduced to a binomial process to resolve problems. For example:


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 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.