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Format: VoseBinomial(n, p, U)
A Binomial(n,p) 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 the same 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 modeling of binomial processes, many other stochastic processes can be usefully reduced to a binomial process to resolve problems. For example:
Binomial process:
Number of life insurance holders who will claim in a given period;
Number of loan holders who will default in a certain period;
Number of false starts of a car in n attempts;
Number of faulty items in n from a production line;
Number of n people randomly selected from a population who will have some characteristic;
Reduced to binomial:
Number of machines that last longer than T hours of operation without failure;
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 that use the binomial distribution:
Distribution fitting of threshold data
The Conditional logic example uses the binomial distribution.
The Binomial distribution makes the assumption that the probability p does not change the more trials are performed.
Another example: the number of faulty computer chips in a 2000 volume batch where there is a 2% probability that any one chip is faulty = Binomial (2000, 2%).
The Binomial distribution was first discussed by Bernoulli (1713). It is related to the Beta and 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(1, p) that is used to model risk events.
The Binomial distribution has the property Binomial(n, p) + Binomial(m, p) = Binomial(n+m,p) which makes sense if one thinks of n and m being two sets of independent binomial trials, all with the same probability of success.
When modeling or analyzing counting data, it is often desirable to modify probability of zero of the discrete distribution we use, to more accurately model the probability of "no event occurring". We can make two types of modifications to our distribution for this:
Zero-inflated model - we increase the probability of zero. (equations)
Zero-truncated model - we entirely remove the probability of zero events occurring. (equations)
See also: Zero-modified counting distributions
VoseBinomial generates values from this distribution or calculates a percentile.
VoseBinomialObject constructs a distribution object for this distribution. Professional and Industrial editions only.
VoseBinomialProb returns the probability mass or cumulative distribution function for this distribution. Professional and Industrial editions only.
VoseBinomialProb10 returns the log10 of the probability mass or cumulative distribution function. Professional and Industrial editions only.
VoseBinomialFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution. Professional and Industrial editions only.
VoseBinomialFitObject constructs a distribution object of this distribution fitted to data. Professional and Industrial editions only.
VoseBinomialFitP returns the parameters of this distribution fitted to data. Professional and Industrial editions only.
