# Probability Function Structure

A probability function structure is a function structure that represents an abstract probability function (with a probability value for every probability event).

**AKA:**Probability Distribution Instance.**Context:**- It can (often) be associated to a Probability Function Family/Statistical Metamodel.
- It can range from being a Discrete Probability Distribution Structure to being a Continuous Probability Density Instance.
- It can range from being a Univariate Probability Distribution Instance to being a Multivariate Probability Distribution Instance.
- It can be represented by a Probability Distribution Data Structure.
- It can range from being a Heuristic Probability Function to being an Empirical Probability Function.
- It can be produced by a Probability Function Generation Task.

**Example(s):**- a Graphical Statistical Model Instance.
- a Prior Probability Distribution.
- a Posterior Probability Distribution.
- a Conditional Probability Distribution.
- a Marginal Probability Distribution Structure.
- {(Heads,0.45), (Tails,0.55)} for a Coin Toss Experiment.
- {(0, 0.674%), (1, 3.369%), (2, 8.422%), (3, 14.037%), (4, 17.547%), (5, 17.547%), (6, 14.622%), (7, 10.444%), (8, 6.528%), (9, 3.627%), (10, 1.813%), (11, 0.824%), (12, 0.343%), (13, 0.132%), (14, 0.047%), (15, 0.016%), (16, 0.005%)}, a Poisson Probability Distribution with 5 as the average number of objects per unit volume or events per unit time. http://www.graphpad.com/quickcalcs/probability1.cfm
- a Normal Distribution, associated with a Normal Probability Function.
- a Uniform Distribution, associated with a Uniform Probability Function, such as
- {(Heads,0.5), (Tails,0.5)} for a Fair Coin-Toss Experiment.

**Counter-Example(s):****See:**Bayesian Prior Probability, Statistical Model.

## References

### 2009

- http://www.teacherlink.org/content/math/interactive/probability/glossary/glossary.html
- Probability Distribution: The set of probabilities associated with the values in a random variable’s sample space.