---
title: "Binomial"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575204/Binomial"
format: markdown
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Binomial(p,n)

[Binomial Equations](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575894)

[Crystal Ball parameter restrictions](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575571#CrystalBallfeatures-Beta)

 

 

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

 

![image](media://522837e3-22b2-40c6-af6d-87e719df3a00)

 

### Uses

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](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575354)).

 

The binomial distribution has an enormous number of uses. Beyond simple [binomial processes](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575354), many other stochastic processes can be usefully reduced to a binomial process to resolve problems. For example:

 

Binomial process:

Number of false starts of a car in n attempts;

Number of faulty items in n from a production line;

Number of n randomly selected people with 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](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575262#ApproximationstotheHypergeometricdistribution-AHD) to a hypergeometric distribution

 

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

 

[Conditional logic](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575459)

[Sampling from a liquid](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575642)

[Distribution fitting of threshold data](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575401)

[Bayesian prior](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575397)

[Test result](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575400)

### Comments

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.

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 (2%,2000).

 

The Binomial distribution was first discussed by Bernoulli (1713). It is related to the [Beta](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575217) and [Negative Binomial](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575213) distributions, all of which have their basis in the [Binomial process](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575354) where the Binomial distribution is also derived. The [Bernoulli](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575202) 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.

 

The Binomial distribution has the property Binomial(p, n) + Binomial(p, m) = Binomial(p,n+m) which makes sense if one thinks of n and m being two sets of independent binomial trials, all with the same probability of success.

 

The Excel function BINOMDIST(s,n,p,**0**) returns the binomial probability mass function, and BINOMDIST(s,n,p,1) returns the binomial cumulative distribution function.

 

 

 

 

 

 

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